hyperbolic crochet

in case you missed these...

2012-01-26T23:36:00.000-05:00

James Moriarty - you heard this name, don't you? Most of us know him as a greatest adversary of Sherlock Holmes. But did you know that Moriarty was a mathematician of exceptional gifts?
In the latest Holmes flick, Sherlock Holmes: A game of shadows, they don’t just need their trusty revolvers and Holmes’s trademark prescient fight scenes, they also need to grasp some mathematics. (So far I have seen only the trailer which looks like too much Holiwood thriller...)
More about the movie here. In Wikipedia you can find some things about Professor Moriarty -
there has been speculations " that Doyle based his fictional character Moriarty on the American astronomer Simon Newcomb. Newcomb was revered as a multitalented genius, with a special mastery of mathematics, and he had become internationally famous in the years before Doyle began writing his stories. More pointedly, Newcomb had earned a reputation for spite and malice, apparently seeking to destroy the careers and reputations of rival scientists.^"
Would popularity of Sherlock Holms stories contributed in part of general public the perception of mathematicians (and mathematics) as something evil?
There are dark biographies of mathematicians - for example, one of André Bloch,Ted Kaczynski. But now there is the most recent sad story about Oxford University math professor who was suspected in murder of his friend and fellow professor Rawling. Here is this story from The Guardian (Friday, January 13, 2012). Some British newspapers say that "the two had an altercation over an academic issue that got physical". In Telegraph this story is put in more reasonable perspective - math professor was treated wrongly by the police. Prof Rawlings wife issued a statement that "it has been a ragic accident", most likely Steve Rowlings (who was one of a handful of figures who helped bring the Square Kilometre Array (SKA) – which will peer back 13 billion years in time – to the brink of construction) died of a sudden heart attack due to extreme stress he had lately.
I enjoyed watching Inspector Lewis series on PBS which takes place in Oxford. May be this latest event will make it into another Inspector Lewis episode....
Talking about mathematics and movies - here is a nice link to the list of movies with math in them:
Mathematics goes to movies
In the latest issue of Cabinet Magazine (issue 44 Winter 2011/2012) there is a history of one of the most popular "math movies" Powers of Ten.
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Some interesting applications of math:
The theorem that provides continuity for space, time, and airport maps
and The math behind screening tests.
But the exhibit I am putting on my calendar to see is in NYC - Chelsea -
Curved Crease Sculptures by Erik and Martin Demaine.

Erik Demaine explains curved creased sculptures and surprisingly old history of these sculptures.

Colorful Winter

2012-01-15T00:00:00.000-05:00

Snow in Riga started to fall on Friday, January 13. My family here had a visitor from South Africa who came to see the snow for the first time in his life - so he had to wait until the day of his departure... My first day in Riga was wrapped in a fog.

The title "Colorful Winter" is the name of a show in Riga which I enjoyed very much - not only because it is really colorful and artistic, but also it made me happy that traditional Latvian craft skills are still kept alive and developed further. I am so proud to show you - these are traditions from a country where I was born. I have to confess that this exhibit made me long for my knitting needles so much that my shoulder started to ache as to remind me - not yet.... :-(

Math and Art in Joint Math Meetings 2012

2012-01-13T16:14:00.002-05:00

Boston was the the meeting place for about 7000 mathematicians - if I am not wrong it was the record number.
Even NPR featured this meeting on All Things Considered.
I was in Boston to accept 2012 Euler Book Prize. It felt really special to be on the same stage with famous mathematicians, but particularly with Bill Thurston. Here you can see the full Prizes and Awards booklet.
The Art Exhibit in this meeting has become traditional and well received. It is a juried exhibit and here is info about this year awards , there is also a video about it:
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Some of my own pictures will follow - delay in posting them is because stright from Boston I travelled to Riga where I am now un til January 21.

Not featured in this JMM 2012 art exhibit but nevertheless artistic and hyperbolic is this animation of hyperbolic Christmas ornaments featured in New Scientist.

Happy MMXII !

2011-12-31T00:00:00.000-05:00

Happy Holidays and Newton's Day!

2011-12-25T18:48:00.001-05:00

Did you know that today is also Newton's Day? He was born on Christmas Day but because of calendar changes his birthdate has been moved around. Anyway - it is good to know that Cambridge University has digitized Newton's papers and they can be seen here:

Cambridge Digital Library

Mathematics elsewhere

2011-12-17T00:27:00.005-05:00

Thank you for all the greetings about Euler Prize! I remember how news spread about my book winning Diagram Prize - in a day it was around the globe - the oddest title of 2009 is Crocheting Adventures with the Hyperbolic Planes. :-) News about Euler Prize are spreading slowly but I have found some nice mentions of the book:in German Science Blog, (author does not know that one of my crocheted planes is in Germany right now - in a show in Darmstadt), Edinburgh Science Festival (I was in Edinburgh when I was writting the book, and there are pictures from there in a book!), Images des mathematiques - (this was actually the first one after MAA anouncement).

Talking about France - there is unique exhibit there now - Mathematics:A Beautiful Elswhere

On the other side of Atalantic a mathematical art contest "This is My Math" organized by McGraw-Hill was for very beginners in art and in math :-) - hopefully early start will keep young minds longer focused on math.

Robert Fathauer's art exhibit Ars GEometrica is open in Budapest, December 5-February 24, 2012.

Digital print. Image size 11" x 14". 2004. Robert Fathauer

Knitted Napier's Bones by Pat Ashworth, Ben Ashworth, and Steve Plummer:

here is how to use them, but if you want to see more of their awsome designs go to Wooly Thoughts

Recently I learned that Google is showing some love to math lovers.
I do feel know like compiling "news digest", which is perhaps news for me because the end of the semester was so full that I did not have much time to spend online. Just one more new link - this is for crocheters - Ancient patterns digitized. Enjoy!

2012 Euler Prize!

2011-12-13T10:51:00.000-05:00

It is my great surprise and honor to announce that "Crocheting Adventures with the Hyperbolic Planes" are chose by Mathematical Association of Americas to receive 2012 Euler Prize.

My online exhibit

2011-12-06T22:46:00.001-05:00

I created my "online exhibit" - please visit:
Daina Taimina - Fiber Sculptures

Happy Thanksgiving!

2011-11-24T21:04:00.001-05:00

It is already Thanksgiving! Time has gone very fast and I truly had no time for a blog.
However today is a day for thanks and I sincerely wish to thank all of you who visit this blog!

On of my works is in a show Entlang des Fadens: Das Textile als Medium der zeitgenössischen Kunst at Kunstarchiv, Darmstad. Another little piece made its way to Sicily and is included in interesting project Crochet-Itinerante. Here is this project so far:

I am very happy that Helen Tian volunteered to help me with crochet for my next project. My shoulder still is not allowing to crochet too much - I tried to finish some project and at least could crochet some. Looking through my other projects I found one unfinished knitting one. Well, I have a volunteer helper for that one also:

My creativity has been suspended due to teaching this semester and numerous appointments with people who are helping me to get my shoulder to work properly. Can creativity in math be compared with Shakespeare? Here is a video where few men are discussing this issue - interesting that they did not think about inviting any woman to this discussion...
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If you want to spend more time on this issue - here is 90 min program Mysteries of the Mathematical Universe.

Some interesting links:
Leonardo's Formula explains why trees don't splinter
Wired has published what they think are 9 equations every geek should know
Adventures in N-th Dimension

and this one:

the capitalist network who owns and rules the world

11.11.11

2011-11-11T11:11:00.000-05:00

Nature wants to be "hyperbolic" - to have negative curvature to withstand great depth -
Scientists plumbing the depth of the Mariana Trench - the deepest part of the ocean on the planet - have identified gigantic amoebas lurking miles and miles beneath the waters.
The creatures are called xenophyophores, and scientists from the Scripps Institute of Oceanography at UC San Diego spotted them in the cold, crushing depths 6.6 miles beneath the white caps.
(Discovery News)

Tumultous ocean is quite different from this beautiful mirror symmetry last Sunday at Walden Pond

A lake is the landscape's most beautiful and expressive feature.
It is Earth's eye; looking into which the beholder measures
the depth of his own nature. - Thoreau
from the chapter "The Ponds" in Walden

RIP Steve Jobs!

2011-10-06T00:06:00.002-04:00

"We're here to make a dent in the universe. Otherwise why even be here." Steve Jobs

Bill Thurston - some thoughts about mathematics

2011-08-30T22:13:00.000-04:00

These are exercepts from Bill Thurston's notes for the seminar Topics in Topology which started on August 29, 2011 (used by permission from the author).

Mathematics often progresses in waves, where flocks of mathematicians cluster around topics that are currently undergoing rapid development, or have recently seen big developments. Group cohesion is maintained by conferences they attend, as well as visits, talks, and collaborations. They often know many of the same mathematical ideas, and it is common for mathematicians to mainly tune out for topics outside their shared knowledge of their flock. Some mathematicians participate in two or more flocks. Going against the flocking trend, there are also many mathematicians who work in a more solitary style, often persevering doggedly on topics they've become fascinated with. They often participate in one or more flocks, but they maintain an interest not widely shared by their peers.

Here is one downside of the flocking behavior: a great part of the propogation of mathematical understanding is by face-to-face discussions and oral tradition, because mathematical papers are often much more technical, tedious, and denatured compared to how people really think about the ideas when they are actively working on them and developing them, Participants in a flock read each other's papers, but often this is made much easier and more natural because fo their shared background. It is much harder for someone not already versed in the basics of a topic to understand from a technical paper what it is all about. Different flocks use different language to discuss similar mathematical phenomena; people have a big decoding problem when they jump to papers written in a different tradition.

We take in things geometrically bu do not really have adequate ways of communicating these things in the same way.

Mathematical tradition has a vast breadth. My experiences have led me to believe that in principle mathematics is quite unified, with almost any topic potentially connected to almost any other topic, but that the connections are often disguised and undeveloped.

I didn't start out with this mental image of mathematics as highly connected. As an undergraduate and graduate student, I had many interests that would distract and divert me, and that I wanted to pursue. I became frustrated by all the loose ends, and I had a mental image of mathematics (and science) as something like a tree, or perhaps like a hyperbolic space, spreading out exponentially in a quickly unworkable number of directions. .... I often found myself getting sidetracked by some question or remark a professor or fellow student would throw out, and I'd spend days trying to work out an understanding of a small question or topic thjat I became fascinated by. I'd chide myself for wasting my time, instead of following along and giving more mind to the important things I was supposed to be learning.
At the time, I didn't think the side topics led anywhere special, but over the course of my career, again and again, the mathematical side-branches that I pursued enough to gain some insight have connected, often in significant ways, to other more mainstream branches of mathematics that I was interested in. I've seen enough occasions where I or others developed surprising interconnections that I think potential connections are quite common.
A major difficulty in the development of connections is not only that there is limited intermingling between different flocks of mathematicians, but also flocks, like individuals, have a limited life-span: topics and points of view often disappear from sight as flocks of mathematicians dissipate and move on to fresher feeding rounds, and solitary mathematicians also move on or go out of circulation.

Mathematics is about teaching human brain how to think. When your brain is educated, your can see much more interesting things and connections.

These thoughts echoed with the Forward Bill Thurston wrote to my book Crocheting Adventures with the Hyperbolic Planes - it is possible to read it by clicking Look Inside!
W. Thurston On Proof and Progress in Mathematics
Mathematical Education

About photos: first one is in Stewart Park, Ithaca, NY, the others are from my recent trip to Canada.

where "hyperbolic crochet" started

2011-08-10T07:08:00.000-04:00

Yesterday I came back from Pennsylvania. I was at the place where I started to crochet hyperbolic planes. The very first one was crocheted in June 1997 during geometry workshop in Cornell University, in Ithaca, but the next one and the first model of hyperbolic pair of pants where crocheted in our camping place in the picture above. The tiny cabin is gone, only its former place still can be seen. No memorial signs :-) .

The outdoor kitchen and "dining room" our family was using then is still the same, just by now two cabins at both ends of it are added.

This swimming pool which is used by all community members is also essential in early history of crocheted hyperbolic planes - in summer 1997 I spent many hours at the pool side while my two daughters were learning to swim and improving their English. We arrived in United States just before Christmas in 1996 and they did not know any English. When in fall of 1997 they returned to school, they had no more problems with American English and were correcting me who was taught to speak a proper British.

This is a view from the poolside in Mc Corkle Tree Farm I was watching while crocheting hyperbolic planes for my upcoming class in Cornell.

The only "hyperbolic" thing one could find there this time.

beauty in mathematics

2011-07-26T12:28:00.001-04:00

I am teaching a course this summer in Cornell called Prove It! Very intense - in 6 weeks we are covering equivalent to one semester. Not much time for blogging because I have never taught this course before and I do want to show my students some elegance in mathematical proofs and in mathematics. Today we are talking about the proofs, and this is a picture of E8, more about it here.

Just couple more recent links on beauty of mathematics:

The Unreasonable Beauty of Mathematics

Aperiodical Tilings in Mexico City

Gardening by the Numbers

Some cool videos about math and art connections from MoMath

different results of American math education

2011-07-24T22:43:00.008-04:00

Here is quite different example - The Art of Mathematics. Dorothea Rockburne has found inspiration in her lifelong deep interest in mathematics. Geometry of Diverse Career

what's new

2011-06-13T23:10:00.001-04:00

There is such an amazing talent and creativity in the world and it is great to see it any possible ways to come out. In Pasadena now until August 21st in Williamson Gallery will be an exhibit Hyperbolic: Reef, Rubbish, Reason. In Pasadena Star there is a nice review and pictures from the show. Crochet Coral Reefs keep growing - currently The Maine Reef is growing, crocheters are busy in Asheville and Honolulu.

I have some new ideas and my fingers are itching to start a new piece ,but ... my creativity has to turn back to teaching mathematics - on June 27th I will start teaching six week course Prove It! which I have not taught before and this is first time when it is offered in Cornell Summer session. My right arm is still hurting. No crochet or knitting for a while - it is hard enough to type. I am working on getting my arm to be able to write on a board - still teach old fashion way :-) I am very hopeful to avoid surgery but have to have another cortisone shot to cut inflammation so I can do more exercising it. Crocheting is not included on that list. At least I can still take pictures and learn about some amazing talents.

I was in New York City before the heat wave, so Saturday was pleasant. Did not know that there was some unusual art opening in Manhattan - toddler Aelita Andre has an art exhibit and that night 9 of her paintings were sold for $30 000, more here

here is a video:

How many more such "prodigies of color" we would have if more children could have such an exceptional opportunity to play so freely with colors?
Next day - Sunday night, June 5th, we turned on TV PBS station and there was a concert - the star was another child Jackie Evancho who will have her CD "Dream with me" release tomorrow. This is a video of her performing Nessun Dorma:

Geometric Manifolds for Hyperbolic: Reefs, Rubbish, Reason

2011-05-19T08:40:00.000-04:00

Yesterday seven of my works started their way to Los Angeles where they will part of the exhibit Hyperbolic: Reefs, Rubbish, Reason. The show curated by The Institute For Figuring will be held at Art Center College of Design in the Williamson Gallery, June 6-August 21, 2011. The IFF has decided that it will be the last major Reef show they do and at the same time it'll be a homage to hyperbolic geometry.

Why there are more than seven pictures? Manifolds come in different forms and shapes and we have to train our eyes to recognize them, so - which are the seven different ones?

toujours penser à Paris

2011-05-15T16:04:00.000-04:00

Still thinking of Paris and keeping up with my little French learning new words and expressions. I found a great helper in that - Kristin Espinasse's book Words in a French Life based on her blog French Word a Day. This book is helping me: learning French words and expressions; learning from an experienced blogger, and her cultural comparisons - American versus French - is prompting me to go over my own experience adapting to American life. But that would be a different story.... These are "out of date" memories but I have been trying to keep away from my computer - one of the things I have to do to encourage my shoulder to heal. I returned to exercises in pool, going to physical therapy, keeping up with exercises at home and going for long walks. But today is so rainy day that nothing can be done outside and it is Sunday, so I decided to open a picture folder called Paris and to look into sub folder named street scenes.

I still have seen the Statue of Liberty in New York City only from Staten Island ferry or Manhattan, but in Paris had a chance to get close to it. In appreciation for the Statue of Liberty in New York harbor, on July 4, 1889 Americans living in Paris erected a small replica, about 35 feet high, of the Statue of Liberty. It is mounted next to the Pont de Grenelle, a bridge crossing the Seine, 1.5 km South of the Eiffel Tower. Not too many tourists obviously try to get close to this statue, so there is a camp of homeless people next to it. But there is actually quite nice walk on Isle de Grenelle towards the Eiffel Tower that allows to appreciate the ironwork and sculptures on bridges.

To get around Paris the best way is to buy Paris Pass. Which one to choose, really depends how long one is staying. We had weekly passes and it is good to know that instead of sightseeing bus, you can choose Bus No.69 which covers most of "tourist objects". The other option is to walk around which I enjoyed a lot. To drive in Paris is possible - there are lots of cars on streets, but you can choose this option if you have superb parking skills. Some examples of necessary parking can be seen in pictures.

If your car is an art work, then may be you are allowed to park in No Parking zone

No wonder that people choose to live on Seine where parking is not so complicated as on streets. Some of these houseboats are for rent - approximately 470 euros for 2 nights...

Some houseboats even have a little garden, modern kitchen and fireplace...

During our stay in Paris we were more traditional and rented a studio apartment in Le Marais, near Hotel de Sully, across from Eglise Saint Paul and next to Metro station Saint Paul (opened in 1900). Staying in the apartment gave some illusion of "living in Paris", of course, walking on the street I was missing necessary companion, so I could not pass for la véritable parisienne.

These little friends are cute and I do like dogs but I could not stop to wonder in Paris how come that these little dogs are leaving so big piles after them. These fancy ladies did not have any plastic bags or desire to clean up after their showpieces.

Well, streets are being cleaned by running water - they just open faucets and let a stream of water to run and wash everything away. I do not know how often it happens, so watching your step while walking in Paris is useful.

Sometimes walking can take to unexpected places like this little path next to Palais Decouverte - Paris Science Museum since 1937. I mentioned it in one of my previous entries.

I felt like I am entering a secret garden.

I noticed two middle age people a man and a woman. First I thought that they were here on a date but then I noticed - they were not talking but watching something, and I decided to satisfy my curiosity. The creature they were observing was a muskrat.

The man soon left, and the woman looked at me and finding me trustworthy took out a carrot from her bag. The muskrat obviously was expecting this move and gladly accepted the treat. I said in French

Il reconnaît vous. The woman answered me that yes, she comes here every day. I felt excited that I have a chance to practice my minimal French but not for long. The woman switched to English and told me that she teaches philosophy in Sorbonne and visits this place on her way home. She was kind but soon I felt that I am interrupting her connection with her pet and I walked away.

The sun was going down, and it was time for me "to go home" to prepare for "opera night".

crochet, architecture, design

2011-05-05T17:47:00.002-04:00

Last August I wrote about the talk I attended here in Cornell about using crochet in architecture studio. On Tuesday I was visiting Gisela Baurmann's seminar with two purposes. One was by Gisela to explain to students more about geometry they had used in their projects, the other - I was so curious to see what they all have created. The whole set of pictures from the seminar can be seen here. I am taking from there some examples what can be created with crochet and 3D-printing.

I like this quote from Gottfried Semper who in 19th cnetury was seeing creative possibilities of various stitches and their possible applications in architecture but his ideas at the time were called eccentric:

The loop stitch is a noeud coulant: a knot that, if untied, causes the whole system to unravel. It is an element in making stockings, in knitting and crocheting, and the particular way it is formed is dictated by the tools employed and the use intended. […] I can only say that it is an extremely refined [art] and yields products whose properties can be achieved in no other way. They carry the elements of their richest ornaments in themselves and in their construction. Elasticity and ductility are the specific advantage of these products; this makes them especially suited to close-fitting dressings that embrace the figure and define it without fold.

--Gottfried Semper, ʻStyleʼ, 1860, Getty Publications (2004)

These models reminded me Romanian designer Radu Comsa who saw my work in 2005 and was inspired to use it in design and created Rasta Stool ( referring to Rastafari):

He continued to explore hyperbolic geometry and now is calling this direction hyperbolism.

Wnat to make some hyperbolic design? If you have enough patience try this:

Learn How to origami a beautiful hyperbolic arch. For more Origami How-To Videos & Articles, visit WonderHowTo.

If not making hyperbolic design by origami, you can choose to do it with computer like Kerrin Jefferis and Patrick Stein - Computational Nature Study for Generative Design (Masters of Digital Design, University of Canberra) did in their project Hyperbolic Coral

They even created matrix to visually show how the shape changes by changing the ratio of increases:

Here is another application of negatively curved surface (pseudosphere)

Actually National Geographic and New York Times has serious news how 52 years and $750 million spent on proving that Einstein was right... And we see pseudosphere once again!

My work in Cooper -Hewitt National Design museum

2011-05-01T22:14:00.000-04:00

My work has been included in Cooper-Hewitt National Design museum Textile collection. It will be displayed only in 2013 when museum will re-open after an extensive renovation. Ithaca did not have many sunny days this spring, so I had a brief chance to take a picture of the piece before sending it away. Here it is:

There will be another one which viewers will be allowed to touch

Mathematicians in Paris - V

2011-04-21T17:16:00.001-04:00

David Eugene Smith (from columbia.edu)

David Eugene Smith, whose Historical-Mathematical Paris (1923) I was my guide in some of walks in Paris, started his notes with the epicenter of Paris Île de la Cité. So far in my story I have wondered from there to the intellectual Left Bank. Now it is time to remember that on the Île de la Cité near the North Tower of Notre Dame until 1748 was the small church of Saint-Jean-le-Rond on the steps of which Jean le Rond d'Alambert was found.

Jean le Rond d'Alambert (from Wikipedia)

I first learned about d'Alambert as a freshman in university when we studied limits and used d'Alambert's ratio test. A little snapshot about him prompted me to find more and I looked for his biography (no Internet those days! :-) ). I became fascinated by his many talents and interests (not so much with his personality). Geometry stayed d'Alambert's favorite subject as he wrote in 1777 letter to Lagrange:

What annoys me the most is the fact that geometry, which is the only occupation that truly interests me, is the one thing that I cannot do. All that I do in literature, although very well received in our public sessions of the French Academy, is for me only a way to fill the time for lack of anything better to do.

While connected with French Academy of Sciences on the Left Bank, d'Alambert was a frequent guest at M-me Geoffrin's salon at No.374 Rue Saint Honore. Later he moved in the house of another well known hostess of her own salon Julie de Lespinasse. I will return to places on Rue Saint Honore later.

(from Wikipedia)

Monk and medieval philosopher Abailard had his cell on Ile de Cite - he studied Euclid in connection with his own lectures in logic. It is hard to tell how much geometry studies occupied his time or whether he used them to keep his thoughts away from his beloved Héloïse, who was first his brilliant student and later became known for her own exceptional scholarship. Perhaps their love letters is the origin of romantic love, they are revealing us one of the most celebrated love story. Six hundreds years later Josephine Bonaparte was so moved by this order that she arranged for the remains of both lovers to be together at their final resting place in Pere Lachese cemetery.

Mausoleum to Monge in Pere Lachese cemetery

(Mathematicians buried in Pere Lachaise cemetery are: Arago, Poinsot, Delambre, Monge (interred to Pantheon but his mausoleum still there), Hachette, Fourier, Chasles and founder of positivism and sociology Comte.)

Some places of historical-mathematical interest on the Right Bank:
On Rue de Rivoli you cannot miss 52 m tall tower - Tour Saint Jacques , all that remains there from former 16th century church. Blaise Pascal replicated Torichelli's experiment with barometer there - carried it up to the top of the tower and checked that mercury level has dropped. Pascal's statue now is at the base of the tower.

In 1979 I saw Pascal's calculator in Zwinger Museum in Dresden, this time I missed the opportunity to see the other copy signed by Pascal in Musee des Arts et Metiers. This museum is on my list to visit next time I am in Paris.

The Palais du Louvre is known first and foremost as a museum which houses one of the most stunning collections of artworks in the world. Yet for almost seven hundred years the buildings constituted one of the principal residences of the kings and emperors of France. It became museum in 1793 and at that time the art collection was not large enough to fill all complex, so part of it was used for government offices and even residencies. For example, mathematician Legendre was asking for quarters for himself in the older part of the Louvre.

On a rainy day it was great to visit Louvre and to walk through it not rushing. We could look at the details and notice mathematical constructions in architecture or in famous artworks.

This time though we did not try to check all the possible uses of golden ratio in Venus de Milo or Mona Lisa like we tried in Milan couple years ago when finally got a chance to see The Last Supper and then alerted security guards performing suspicious activities by their standards. I was trying to follow straight lines with my fingers in front of my eyes to check whether they really intersect in a point just above the head of Jesus, David used his notebook to locate the vanishing point more precisely. Security guards surrounded us and demanded to inspect our hands. After they found nothing, they stared at us very puzzled. Then I politely said that we are mathematicians, which they took as some particular medical diagnosis.

I wish I would've come to Paris with my children when they were very young to show how much math is there around. This thought came in mind again today when I read David Bornstein's A Better Way to teach Math - "...very early in school many kids get the idea that they’re not in the smart group, especially in math. We kind of force a choice on them: to decide that either they’re dumb or math is dumb." Imagine walking in Paris with a little curious mind and big eyes next to you. In front of Louvre there will be a question - what is this big glass thing? Imagine all the different stories you can tell about pyramids - mathematical or not.

How about asking question whether these are also pyramids on the wall of this new building? Or - what is a diagonal? That answer I would know how to answer but I would not be able to answer next logical question - why the supermarket is called Diagonal? In middle school geometry class students have hard time learning all those various geometric terms. Don't you think it would be great idea to call various offices in school in those names? It always helps to remember when you have associations connected to the term.

I can imagine some more questions -why this is Point Zero? What is zero? What it means omega? What is the symbol next to that word?

Indeed, I am getting carried away from what I started to write about. To speed thin gs up in my description I will just now quote David Eugene Smith about places connected with Voltaire and marquise du Châtelet

In the frontispiece to their translation of Newton, du Châtelet is depicted as the muse of Voltaire, reflecting Newton's heavenly insights down to Voltaire.

- translator of Isaac Newton's Principia Mathematica in French. Returning back to my earlier thoughts of early childhood education and underestimating children abilities to learn - Emilie du Chatelet was fluent in Latin, Greek, Italian, and German by the age of 12.

From David Eugene Smith's Historical-mathematical Paris:

If we rank Voltaire in our guild because of his work on the philosophy of Newton, we shall naturally find many spots in Paris connected with his name, and portraits and statues in great number and often of much excellence. The present Rue Moliere, running from the Avenue de l'Opera to the Rue Richelieu, for example, was once the Rue Traversiere, and at the old number 25 was a house which was rented to the Marquise du Chatelet,4 and there Voltaire lived for some time, setting up a little theatre for his plays. Around the corner, at No. 8 of the Rue de Richelieu, the street on which the Bibliotheque Nationale fronts, was the cafe of Charlotte Bourette, who was known as the Muse Limonadiere, and whom Voltaire esteemed for her wit.

Farther up the Rue de Richelieu, at No. 102, stood a house which Voltaire owned and in which his niece, Mme. Denis, lived after the death of the Marquise du Chatelet. Next door, at No. 100, stood the house of Voltaire's friend, Mme. de St. Julien, whom he often visited.

Rue Richelieu No.102

Voltaire also lived (1732 and 1733) at what is now,No. 20, Rue de Valois, in the same vicinity, east' of the Palais Royal. Not far from here, at No. 161, Rue Saint-Honore, is the Cafe de la Regence, which I well recall as still prominent in the artistic life of Paris when I was a boy. (note: DS wrote this in 1923!)

no cafe there anymore

Its predecessor stood a little to the east, at the Place du Palais Royal, and was frequented by Voltaire as well as by Benjamin Franklin, Diderot, Napoleon, and other makers of history. Over on the Ile Saint-Louis, at No. 2, on the Rue Saint-Louis-en-l'Ile, is the hotel (man- sion) of Nicolas Lambert de Thorigny, sometime president of the Cour des Comptes, built in 1680. The Marquise du Chatelet lived there for a time, and Voltaire was, as usual, a guest of the house. His sister, Mme. Mignot, mother of Mme. Denis (to whom Voltaire was greatly attached), lived at No. 133, Rue Saint-Antoine, a continuation of the Rue de Rivoli and leading into the Place de la Bastille.

Hotel de Sully on Rue Saint-Antoine

The Place de la Bastille

Although the Bastille has long since ceased to exist, when the wanderer stands upon its ancient site he may reflect that Voltaire was twice imprisoned there, for his rash utterances on the rights of man. Voltaire was baptized (1694) in the church of Saint-Andre-des-Arcs, which was built in 1210. 2 and her family, Tonnelier de Breteuil, there are various interesting spots connected with each. The family owned a hotel at No. 14, Rue Portefoin, a little to the southeast of the Conservatoire des Arts et Metiers. They also owned (1760) a place at No. 56, Rue des Francs-Bourgeois, near the Palais des Archives Nationales, and somewhat earlier (1728) one at No. 4, Place des Vosges, on the same street. In 1752 the marquise was living at No. 18 of the same Place.

Place de Vosges

It stood on the present Place Saint-Andre-des-Arts,1 near the Point Saint- Michel, and was demolished about 1800. In 1793 it became the Temple de la Revolution. Voltaire once worked as a clerk in the office of Maitre Alain, No. 1, Rue des Grands-Degres, so called from the steps leading down to the quai, and he became a mason in the lodge of the Ne uf Soeurs which stood at No. 80 of the Rue Bonaparte; but the atmosphere of the Quartier Latin was perhaps not so well suited to his maturer years, although he lived for a time in Rue Mazarine and in 1743 was living at No. 23, Rue Fontaine Moliere. He died in the house of the Marquise de Villette, at No. 27, Quai Voltaire, as an inscription states. The present name of the quai, formerly the Quai des Theatins, was given in memory of this event, as was that of the Rue Voltaire which branches off at No. 211. His final resting-place is appropriately in the Pantheon, the Valhalla of France. As to busts, bas-reliefs, and statues of Voltaire, Paris has been over-generous. Houdon's bust in the Comedie Franqaise is the best known, but the statue by Caille (1885) on the Quai Malaquais is also familiar to every visitor to the book- stalls on the Rive Gauche. "

the Comédie-Française

Place Franz Liszt in Paris(from wikipedia)

David Smith mentioned that near Gare Saint Lazare Franz Liszt lived at No. 63 Rue de Provence. The great composer and pianist was supporting the young arithmetic prodigy Henri Mondeux. On April 30, 1841 Liszt gave au benefice de jeune Patre Mathematicien. May be this fact should be more popularized in order to encourage present day music stars to give benefit concerts to support mathematicians, particularly when government is cutting NSF funds.

Maupertuis is buried in Eglise Saint Roch on rue Saint Honore and Lagrange lived at No. 124 rue Saint Honore. I went to explore Rue Saint Honore but nowadays it has become fanciest shopping address in the world may be, so from mathematical world I felt thrown in another type of the world but about it - next time.

New York Hall of Science

2011-04-10T14:13:00.001-04:00

On April 5th I visited New York Hall of Sciences - I was kindly invited to give a talk for the Staff Professional development seminar. I was caught in traffic while driving there from Brooklyn - 11 miles took more than an hour. Because of that I arrived just before my talk and did not have time to look around beforehand. But I did later and saw interesting things.
It is still possible (until April 24) to see a wonderful travelling exhibit 1001 Inventions which previously was shown in Istanbul and London.

So called "dark ages" in Europe was the Golden Age in Muslim civilization. Innovations from that period are still in use today. I liked very much how visitors are invited to push buttons at particular exhibits by mischievous story tellers who wave at you.

One of the stories I listened was about Islamic architecture and developing the infrastructure in cities. It also mentioned amazing geometric constructions which later were copied by Western architects.

The story about the astrolabe is told by woman and this was not the only one about creative and smart women. More can be found on 1001 Inventions website. But this movie will give a better visual idea about this fascinating exhibit:

Director of NY Hall of Science Eric Siegel proudly showed me and David a permanent exhibit Mathematica. It was designed in 1961 for IBM and is the first interactive exhibition devoted to math.

The long wall of math history starts from approximately 12th century.

The first model we both noticed in the exhibit of course is the pseudosphere -surface with constant negative curvature I was just mentioning in my talk.

Sometimes when I talk about hyperbolic plane my audience is asking me where are hyperbolas on it, and I have to disappoint them telling that there are none.
This surface is hyperboloid which also has negative curvature on its surface but the curvature is not constant. It is an interesting surface that can be built with straight steel beams. It allows minimisation of wind cross-section while retaining structural integrity with minimal material. Cooling towers is one of the application examples in architecture.

This is a nice demonstration of stereographic projection.

My favorite depiction of stereographic projection is by Peter Paul Rubens:

When applied in photography, stereographic projection produces fun images.

Pseudosphere can be seen in another demonstration - about planetary motion. It visually shows black hole idea.

Yet another surface with negative curvature (but not constant!) is helicoid as the demonstration of DNA structure shows. (In Crocheting Adventures with the Hyperbolic Planes I wrote about the connections between helicoid and catenoid and have pictures of crocheted models that show this connection.)

The next surface has both - positive and negative curvature (can you see where?).

If this already reminded you about the mathematical models I wrote in my previous post, then the next picture is even closer to art:

I really liked this delicate string model of helicoid tucked in between braid and sphere packing demonstration. I wish it could have its own case to be fully appreciated.

Also Reye Configuration could use more space (some more pictures of Reye configuration). But of course I understand space issues in exhibits...

I was happy to see the visual depiction of one of my favorite geometry theorems - Pascal theorem (sometimes called Hexagrammum Mysticum Theorem). It is a generalization of ancient Pappus theorem, and Pascal found this generalization when he was only 16!

At the time when Pascal was playing with geometry, he had no idea that this theorem will be later mentioned in projective geometry. There is a nice demonstration of projective geometry in Mathematica. This is a configuration how you see it from the side:

And this is what you see when looking to the same configuration through the hole.

Do not see anything? Good reason to go and visit NY Hall of Science yourself! Much more to see than I can show here, for example, some math magic too:

When we arrived at NY Hall of Science there were many school buses and the hallway was full with happy primary school kids. B y the time we were leaving exhibit halls were mostly empty since school day was over. While I am totally agreeing that we should talk to children about science in early age, I was still thinking about the tendency of turning science museums into children playgrounds. What happens to children curiosity later? Is it consumed by computers and video games and we do not see anymore teenagers in science museums? I remembered my first ever visit to science museum. It was in 1994 in Finland - this year Heureka is celebrating 20 years. It is not as old as Exploratorium or Ontario Science Center, which are twice as old, but still Heureka was one of the first. I have not had a chance to visit it again, so I cannot tell whether I would have the same impression now. But in 1994 we all adults had great fun to look at the exhibits and I do remember many teenagers and adults there and exhibits were engaging us. In US I have met with many people working in science centers and they all confirm the same thing I have notices - science centers are places where parents take their children like they take them to the playground, and children behave there as in playground - they play. It is good first to play but there is no follow up. Except for some volunteers I have not seen any teenager coming to science center - who is going to return to the playground? As a result exhibits are being tailored to the kinder garden level. What happens? Like in NY Hall of Science little kids will pass this very nice Mathematica exhibit - it is above kinder garden or primary school level, it will stay in their memory as something impossible to understand and that's it. I wish I am too pessimistic in these thoughts and wrong...

On my way back to Ithaca I was driving across Tapan Zee bridge

According to 2009 AAA report this bridge is "worst of the worst in New York", some say even in the whole country by now. Still in use.

Attitude to safety like this?

If something endangers them these geese will simply fly away. Bridges, education... Well, may be not my business, may be I am thinking about restricted areas like this park - on my way out I noticed the sign that it is "only for the use to Westchester County residents". So much for "free country"...

Fortunately, these ones did not object us walking there.

Mathematicians in Paris - IV (mathematical models)

2011-04-01T17:23:00.002-04:00

When in 1977 I started to teach geometry in the University of Latvia, there was a small collection of old mathematical models with their titles in German on little uniform signs attached to their sides or bottoms - some plaster models and some were string models. All we knew that they were from early 20th century. I remembered those models used in geometry classes when we studied quadratic surfaces. With computers more and more becoming a part of teacher education, the use of the models became old fashioned and they were neglected. Nobody objected when I collected what was left of them and displayed on a shelf next to my desk in an office I shared with three other people. (oh, that office was a big improvement - for my first 5 years as a faculty I shared a desk with two other people...). By then the string models were damaged and the plaster models looked quite sad also, but I still enjoyed to look at them as to little sculptures. I even tricked one of my students to repair one of the string models by promising to count it as a final exam for the class. He happily agreed thinking that he got a good deal. When he arrived in my office 5 minutes before the final exam - as was the deadline for turning in his work - he said: "You knew it! It was easy to take it apart but in order to put it back together correctly, I had to study everything about those surfaces! Well, now I really know them."
When I last visited my former office in Riga couple years ago, models were gone and nobody knew where.
I remembered those models in Latvia when I saw some mathematical models on a shelf in Cornell Mathematics Library. When in 2002 I joined a team in Cornell to develop kinematic model digital library, I discovered that some of the models in the kinematic model collection were purely mathematical and I became interested in the history of models, even wrote couple papers, (the latest).

Universities late 19th century and early 20th century used to have these model collections displayed as in an art museum - you can see it in the picture of Cornell Kinematic model collection at its beginnings as published in Scientific American in 1885. Some places still have these nice model collections and have displayed them, I wish one day to go and see mathematical models in West Point ( Prof Fred Rickey has researched the history of Olivier models) recently I saw nice models in Vassar College. Some of the model collections are digitized, like The Altgeld Mathematical models collection in Illinois.
[It can be tricky to search for mathematical models on the Internet because nowadays mathematical model does not mean only the tactile model you can physically hold in your hands. Google search may return results like "mathematical model of compile time garbage collection". ]
Angela Vierling-Claassen has gathered a list of Collections of mathematical models and also has some notes on Influence of mathematical models on art.

When in Paris, we never made to Conservatoire des Arts et Métiers (on a list for next time!) but we did visited mathematical models collection in the Institut Henri Poincare. Our guides there were Brigitte Yvon-Deyme and Dominique Dartron - thank you both so much for your kindness and your time! (photos of models in this posting are used by permission of Bibliotheque IHP).
In my introduction to Crocheting Adventures with the Hyperbolic Planes I mentioned the International Congress of Mathematicians in 1954. I was trying to find some picture from this Congress but did not have any success before a book was sent to a print. Now I have a picture I would've loved to have in the book - it was the very first thing David spotted on a wall in IHP.

During the library hours anybody can visit the library to see several cases of the models on a permanent display.

‎
With a little wink in her eyes M-me Yvon-Deyme pointed out that most of the visitors come to see models not out of mathematical curiousity but they are people interested in art, particularly the ones who wish to see models photographed by Man Ray. In the 1930s, the surrealists were interested in various geometries. According to Neil Baldwin, Max Ernst "had taken Man Ray to see the objects on display at the Poincare institute in Paris and had photographed them in a deliberately impressionistic style". These are some of Man Ray's pictures.

The last photo is an interesting mathematical object - can somebody come up with the equation describing it?

Man Ray's photographs were published in Cahiers d'Art (May 1936, No. 1-2, p. 21-26.) and the series was first shown at the New Burlington Gallery (June 11- July 4, 1936).
Man Ray very much agreed with Henri Vuibert who wrote in 1912:

To help students see in space, we materialized the major figures of geometry and descriptive geometry. The use of figures in relief would provide valuable aid to education, especially if one was building these figures by the students." (Anaglyphs The geometric . Paris: Librairie Vuibert, 1912, p. 8).

Man Ray returned to these mathematical models about a decade later when he created series of paintings Shakespearean Equations.

Man Ray Shakespearean Equations: Twelfth Night, 1948 :Hirshhorn Museum

Man Ray Shakespearean Equations: King Lear, 1948: Hirshhorn Museum

In this excerpt (part 5) from Jean-Paul Fargier documentary about Man Ray notice how photos of mathematical models are transforming into paintings. Some more mathematical models appear in part 7.

Surrealists interest sparked public interest about IHP mathematical models and since then the models of the IHP have participated in many exhibitions starting with the one at the Palais de la Découverte, built for the Exposition Internationale des Arts in 1937.

On a personal note here I should add that my interest about 1937 exhibition was because of mathematical models and surprised I discovered that famous sculpture Worker and Kolkhoz Woman by Vera Mukhina (born in Riga!) was the centerpiece of Soviet Pavillion in this exhibition. For me that sculpture always associated with the VDNH (Exhibition of Achievements of the People's Economy) in Moscow and also with the opening of Mosfilm movies.

Here are some of my photos of mathematical models in IHP in Paris.

These constant width solids caught my interest because they are generalization of the curves with constant width.

Among all of the IHP mathematical models there will now also be a place for crocheted hyperbolic plane :-)

PS. Geometry continues to be the inspiration for artists - as one can see it in current exhibit Geometric Days.

Mathematicians in Paris - III

2011-03-27T23:13:00.002-04:00

The Eglise Saint-Germain-des Pres gave its name to the whole quarter around it (which is also part of Latin Quarter). The church was the intellectual center of Catholic church until French Revolution when the church lost most of its power but the intellectual traditions in this area lived on. We walked into this church to look for Rene Descartes resting place. He had many addresses while he was alive, and his remains also travelled - first he was buried in Sweden, where he died, then later transferred to Paris - to the Eglise Saint Etienne-du-Mont, later to Eglise-Saint-Germain-des-Pres (some sources say that only his heart is buried there). In 1792 it was decided that Descartes should be interred in the Pantheon but nothing has changed so far - his "final address" is still the Eglise -Saint-Germain-des-Pres, between two scholarly monks.

Next to the church is a little garden with a sculpture for the poet Guilliaume Apollinaire, who is credited of coining the term surrealism. He thought that " Geometry is to the plastic arts what grammar is to the art of the writer.".

If one would try to put up signs for famous intellectuals who left their footprints in the area of Saint-Germain-des-Pres, then very little space for pedestrians would be left there. On the busy corner across from Eglise Saint-Germain-des Pres I attempted to snap a photo of Les Deux Magots - a cafe that opened in 1875 in the space previously occupied by the fabric shop and which bills itself The Rendezvous of Intellectual Elite. The narrow slice in front of it is called the Place Jean-Paul-Sartre-Simone de Beauvoir. There are several other famous cafes in the area known as traditional meeting places for intellectuals, for example Cafe de Flore, or Brasserie Lipp,

but we, mathematicians, headed for La Procope following its official address 13 rue de-l' Ancienne-Comedie. (Next time I would like to try the other entrance we missed - at 128 Blvd. St. Germain there is an entrance into the lovely passage built by the ancient Paris wall.)

In this "world's oldest cafe" Voltaire and Napoleon Bonaparte have been patrons and that of course overshadows other guests. French encyclopedists were meeting here, among them Diderot and d'Alambert.

We thought that two hours for lunch will be enough time. Apparently not in this place. We were led to the table on the ground floor. While waiting for food to arrive we had plenty of time to soak in the place where discussions among various celebrities (did I mention Benjamin Franklin, Thomas Jefferson, Robespierre, Alexander von Humboldt, Alfred de Musset, and George Sand?) have taken place in the past.

During our lunch I watched a group of visiting German students who clearly were on budget in Paris but had decided to celebrate there stay in a place where authors from their textbooks once had come. Across from us there was an impatient elderly lady waiting for her date. I was curious to guess who would come. My guess that she is a professor was correct (do we all have some professional marks on our foreheads?). Her date was slightly late, and it was her graduate student whom she had invited for a treat, and his lunch was wrapped in a long lecture on philosophical topics.

I used an excuse "to wash my hands" to find that Dames are one floor up, so I had a chance to peak into other dining rooms as well. One of them even has Voltaire's desk.

The name for the street cafe La Procope is on comes from the fact that across from it was the original house of La Comédie-Française.

The sign is quite high up and easy can be missed.
We had to finish our philosophically long lunch and rush to the Institute of Henri Poincare to see mathematical models there, but I will write about it more properly later.
We came back to the Left Bank some other day to look for more places of historical-mathematical interest.
Thanks to David Burke to point out that:
"Saint Germain-des-Pres was not part of the Latin Quarter. They were separate, even rival, entities sharing the medieval Left Bank. Philippe Auguste's 13th century wall ran between them. It ran from the Seine along today's Rue Mazarine, up Rue Monsieur le Prince, looped around (actually just inside) today's Place de la Contrescarpe, and down Rue du Cardinal-Lemoine to the river. That wall was built to protect the Latin Quarter."
In several tour guides Saint-Germain-des-Pres and Latin Quarter are mixed together perhaps because today there is no such strict line between them.

Walking towards Seine rue L'Ancienne Comedie turns into Rue Mazarine. Seems like this is an approximate place of the residence for employees of de l'Academie des Sciences. David Smith in his paper mentioned that Gaston Darboux official residence was at No.3 Rue Mazarine when he was secretaire perpetuel de l'Academie des Sciences.

Rue de Mazarine leads to Institute de France - the most prestigious institution established by Cardinal Richelieu in 1635 as the official guardian of the French language. Under its auspices in 1666 l'Academie des Sciences was founded - to encourage and protect French scientific research. The domed landmark at the end of this street is the Bibliotheque Mazarine - beautiful museum of the books and the working library.

In 17th century Rue Mazarine would be a place where theater companies set up shops at former tennis courts. A plaque on a present day building at No.12 marks the place where Theatre Illustre that lasted only a year but the name of one of its actors, young Jean-Baptiste Poquelin, forever is written in the history of theater. We know him as Moliere.

Rue de Seine was at one time an address of Legendre.

Institute de France

Marquis de Condorcet was wearing many hats. One of them was a mathematician, but he was sentenced to death for his political activities.

On No.2 Rue Christine Laplace lived in 1802. When Gertrude Stein and Alice B. Toklas had to leave their legendary atelier in the Monparnasse, they moved to No.5 Rue Christine, close to the Picasso studio that was just around the corner - at No.7 rue de Grands-Augustins.

Close to Rue Christine is Rue de Savoie where at No. 13 is an inscription that tells that Sophie Germain died there on June 27, 1831.

At the time Victor Hugo wrote his Notre-Dame de Paris (The Hunchback of Notre-Dame) the cathedral was neglected, and even thought to be demolished. Hugo's book was the first work of fiction that brought a city alive, and, as he hoped, the success of the book sparked the public interest and started a campaign to save Gothic architecture. The Eglise Saint-Sulpice is the second largest in the city, only slightly smaller than Notre Dame. The building is very harmonic one, if to ignore two mismatched towers.

The Place Saint-Sulpice infront of the church has the busy Fontaine des Quatres Points Cardinaux in its center. Working fountain in January... For somebody from Ithaca it was hard to believe it is possible in wintertime. This place was beloved place for writers Henri Miller and Anatol France. I believe that some mathematicians have been walking there too, unfortunately they do not usually leave notes about that. Near there used to be the Cafe de la Mairie, favorite of the Surrealists, and of Hemingway, Fitzgerald, and Faulkner, when they lived nearby.

The Marquis de Sade and Baudelaire were baptized in the church of Saint-Sulpice, and Victor Hugo was married there, but these facts were not enough to attract tourists until this church appeared in Dan Brown's The Da Vinci Code.

The book must have annoyed a lot of clergy in the church because next to the famous gnomon there is a big sign that Brown's book is pure fiction. There is also a translation of original gnomon's description.

These gnomons in early days were built in several churches but lost their usefulness after powerful telescopes were invented.

The Baroque chapel on Place de La Sorbonne was commissioned by Cardinal Richelieu and completed in 1635. It is now the sole remaining building of the pre-revolutionary Sorbonne, still the favourite student gathering place. At No.1 Charles Hermitte died in 1901. David Smith mentioned a medallion to Hermitte on the wall of the chapel.

Several mathematicians lived near Luxembourg Gardens. At no.12 Rue de Tournon, near the entrance to the Palais du Luxembourg Cauchy and Leverrier lived. Cauchy was a prolific writer - he wrote about 800 research papers. in the late 1750's on Rue de Tournon at No.27 lived Giacomo Casanova, whose name also associates with large numbers but not the research papers...

The Henri Poincare Institute is near the Luxembourg Gardens. Henri Poincare is buried in Poincare family vault in famous Cemetery of Montparnasse. Other mathematicians there are Gaspard-Gustave Coriolis, Jean Nicolas Pierre Hachette, Urbain Le Verrier.

About our visit at the Institute Henri Poincare next time.

PS. My literary knowledge comes from David Burke's very enlightening book Writer's in Paris.

PSS. March 25 NewYork Times also has a piece about Paris A Paris Farewell by Amy Thomas - sorry if starting March 28 it will not be available...

Mathematicians in Paris - II

2011-03-20T20:22:00.002-04:00

As I mentioned before, my inspiration to find "mathematical" places in Paris came from David Eugene Smith Historical-Mathematical Paris (The American Mathematical Monthly, Vol. 30, No. 3 (Mar. - Apr., 1923), pp. 107-113).
David Eugene Smith (1860-1944) was born in Cortland, NY, just a little more than 20 miles from Ithaca, where I live now. When he died, "the world lost one of the most colorful and influential figures in the fields of the history and teaching of mathematics".(in memorium). Prof. Smith travelled to lecture and to stay in Paris numerous times over the period of 40 years. He was a passionate collector of books, letters and various memorabilia of interest of math historian. From the letters he collected and other sources he learned the addresses of mathematicians in Paris. I was intrigued what I would be able to find 88 years later after his account of "historical-mathematical" Paris was published.
Prof. Smith suggested to start with the most ancient part of the city - the Lutetia, now a part of the Ile de la Cite, where Notre Dame stands. In the ancient Palais de Justice there is a little gem of Gothic architecture - Sainte Chapelle. One of its canons was Rollandus, who wrote a general treatise on mathematics c.1425, now this manuscript is in Plimpton Library, Columbia University, New York City.

There is no need to have a mathematical reason to visit Sainte Chapelle - some say it is the best Gothic architecture example. If you have a choice - go there on sunny day to enjoy the stained glass windows!

This picture on the wall can be a little geometry puzzle:

On the other side of the Palais de Justice it is possible to visit the most ancient prison of the city if interested to see Conciergerie.

The Notre-Dame Cathedral, mathematically, is most interesting for its Gothic arches and flying butresses.

Between Rue Lagrange and Rue Dante there is a little connector which is all what's left from Rue de Fouarre (street of straw bundles) - the most influential street in medieval times on the Left Bank. In 1215 the rebel intellectuals founded the University of Paris. There were no classrooms available, therefore lessons were taught outdoors, with the students sitting on the bundles of straw.(according to David Burke's Writers in Paris) Across from Notre-Dame the oldest trees in Paris shadow the church of Saint-Julien-le-Pauvre.

"Consecrated in 1220, Saint-Julien-le-Pauvre was just nearing completion when the newly established University of Paris began setting up shop next door. And as the university had no buildings, this little church became its chapel and assembly hall. In the 1520's students rioted and trashed the church, so clergy banned firther assemblies. Albertus Magnus advocated for peacful coexistence os science and religion there and his student Thomas Aquinas lectured there (according D. Burke's book). David Smith mentions both of them lecturing in the convent of the Dominicans or Jacobins that from 1217 to 1790 used to be next to place where now is the Pantheon. There is a plague on the wall there too (currently it is the building of the library).

We enjoyed two beautiful piano performances there. One of my favorite piano pieces is Liszt's Hungarian Rapsody No.2. This was the first time I listen to it live in the concert sitting very close to this piano and watching Herbert du Plessis perform. (I was too shy to ask him how many times he had played this piece since his first performance at the age of 8.)

The Pantheon is neo-classic temple built on the highest point of the Latin Quarter. It is a place where French grandes hommes are burried (only two are women - Marie Curie and Sophie Berthelot). In 1851, physicist Léon Foucault demonstrated the rotation of the Earth by his experiment conducted in the Panthéon, by constructing a 67 meter Foucault pendulum beneath the central dome. Mathematicians Lagrange, Lazare Carnot, Paul Painleve , physicist Jean Perrin are burried there, and both Pierre and Marie Curie were enshrined in the crypt in April 1995. Gaspard Monge and Marquis de Condorcet were buried at the time of the bicentennial celebration of the French Revolution.
There is still a monument at Pere Lachese cemetery at the first burial place for Monge.

If you face the entrance of the Pantheon on the left behind it you see the Eglise Saint-Etienne-du Mont where Pascal is buried. Descartes was first buried here also but in 1819 his remains were transferred to the Eglise Saint-Germain-des-Pres.

In this alcove Pascal's neighbour is Racine, the name you will recognize if you are familiar with the history of theatre.

Rue Descartes took me to the Ecole Politechnique, which was founded during the French Revolution by two mathematicians - Lazare Carnot and Gaspard Monge and has always been one of the most elite schools as one can see from the list of notable Ecole Politechnique alumni.

If somebody knows whose portraits are those above the name of the school, please let me know.

Rue Descartes took me to the Place de la Contrescarpe which was the center of the area that in Middle Ages lay outside the city walls. It has long been a haven for outsiders, real and fictional. It was this area described by Balzac in his Le Pere Goriot, one of my required readings in high school. It was this area where young Ernest Hemingway with his wife Hadley had his first home in Paris.

Rue Rollins No. 14 is one of many addresses where Rene Descartes lived.

His famous portrait by Dutch painter Frans Hals (1580-1666) is in Louvre.

According David Smith Rue Rollins No.2 was the house of Marguerite Perier - Pascal's sister, and Blaise Pascal died there.

Returning back to Place de la Contrescarpe I continue my walk on Rue Moufetard, famous ancient market street that has been featured in many literary works by the writers who enjoyed this lively area. It is getting dark, soon restaurants will start to open their door for diners, my thoughts are turning away from mathematical interests towards to the memories of literary descriptions of the area. Another mathematical walk will be next time.
p.s. I am adding here
Paris sites by J. Kiernan (1/26/99) which he posted on Historia Matematica mailing list in 1999.

A good place to begin is the Conservatoire des Arts et Metiers on
Boulevard de Sabastopol. The museum contains one of Pascal's original
adding machines. Near-by are the Archives National. Before you reach
the Seine you will pass Tour St. Jacques. Inside the tower there is
a statue of Pascal commemorating his experiments on air pressure.
To the right is the Louvre which contains a Frans Hals portrait of
Descartes and a Houdin statue of Pascal. As you cross the Seine at the Pont des Arts you will arrive at the Academie des Sciences. Take Rue Bonaparte to the Church of St. Germain de Pres. Inside there is a cenotaph dedicated to Descartes. Follow Boul. St. Germain to the inn La Procope and have the lunch special (if its not dinnertime yet!). In one direction you will find the birthplace of Sophie Germain. If you follow Rue M. de Prince to the end, at No. 54 you will find a plaque commemorating Pascal's (n-1)th domicile. Now follow Rue Sufflot to the Pantheon. Spend some time there. Behind the Pantheon is St. Etienne de Mont, Pascal's church. You will find two plaques and a bust inside. Behind the church is 16 Rue Rollin where Descartes once lived. Continue past Rue Monge to the Jardin des Plants. Inside you will find a statue of its curator, Buffon. Double back to Rue Monge and follow it to the Ecole Polytechnique, the home of an entire class of 19th Century mathematicians. Nearby is the
University including College de France, where Roberval taught, and the
Sorbonne. The University is one of the oldest in Europe and specialized in theology and logic.

On another day you may wish to start out at Port Royal, the refuge of Pascal, and walk to the Observatory which is only open to the public once a month by appointment. Behind the Place Denfert Rocherau there is the Hotel Sophie Germain. Nearby there is a market on Rue Daguerre. Walking down this rue you will pass Rue Gassendi and Rue Fermat. Make a left to Cimetiere de Montparnasse, the burial place of Poincare. On the other side of the cimetiere is Rue Huyghens.

If you visit the Tour Eiffel, you will find several plaques dedicated
to mathematicians. Nearby is 108 Rue de Bac where Laplace resided.
Across the Seine is the Palais de la Decouverte which has exhibits on the history of mathematics. Condorcet met his fate at Place de Concorde.

If you take the train just south of Paris to the suburb of Acueil, you will find many commemorations of Laplace. If you want to see his birthplace, you need to take a train from Gare St. Lazare to Pont L'Eveque. About 7 km away is the small town of Beaumont en Auge. You can walk it on a nice day.

The cathedral at Chartres is a living monument to education. On the West
Portal there are relief personifications of the seven liberal arts. These
include Pythagoras, Aristotle and Ptolemy. Take time to investigate the
circular maze inside the cathedral.

Mathematicians in Paris - I

2011-03-13T19:19:00.001-04:00

What happens when mathematicians go to Paris? For us - me and my husband - the first experience was in Roissy (Charles de Gaulle) airport. While looking for trains to Paris one of our carry-on bags disappeared in a seemingly empty place. Caution - never let the bag handle out of your hand, not even for a second! Besides a little computer and two of my cameras (which I was using for taking pictures for my book) and all other precious things you take with you on a trip (and put in your carry-on bag not to lose!), gone were guide books, English-French dictionaries and my notes of places I wanted to find in Paris. Well, it meant I had no choice but start my "trip planning" over and see what I find as I go.
Paris has long been a magnet for artists and writers - medieval poet-thief François Villon, Molière ("It is not only what we do, but also what we do not do, for which we are accountable"), Voltaire, George Sand, Ernest Hemingway (If you are lucky enough to have lived in Paris as a young man, then wherever you go for the rest of your life it stays with you, for Paris is a moveable feast.), Simone de Beauvoir, Françoise Sagan, Marcel Proust ("...we go off to a city to seek out a soul that it cannot contain but which we no longer have the power to expel from its nature."), Guillaume Apollinaire - just a few names from a long list of writers I have been associated with Paris since high school (yes, I was attending a school for students accelerating in math and physics, but I was reading like crazy - we did not have TV at home...). Paris has honored writers by naming more than 400 streets, squares, or promenades in their names according to David Burke's Writers in Paris.

Mathematicians are also loved in Paris, (not as much as writers though :-) ) but still there are about 100 streets named after mathematicians. There was no way to find all of them, and sometimes I forgot to take a picture of the street sign, but I found some. Already before my trip I saw the post with pictures in The n-Category Cafe and I found some more links:Paris streets named after mathematicians and Photos os street signs by arrondisment. But the real inspiration to find "mathematical places" in Paris was the paper by David Eugene Smith Historical-Mathematical Paris. (I will tell you next time how I tried to find places mentioned there.) (Here is an interesting collection of Monuments on Mathematicians to explore.)

And so - this is Paris:

Not really all of it, just about a quarter may be. Where do you start to get close to Paris? At Point Zero?

Or you try to get up close and personal to some of the images you had in your mind for a long time:

Of course, we went to say "Bonjour!" to the famous lady as did hundreds of others:

It is polite to do so, especially because I had met her in the 1970's when Armand Hammer brought her to Moscow. I have to admit, even if La Joconde is the most famous painting in the world, my favourite da Vinci painting is Madonna Litta in Hermitage Museum, St. Petersburg:

We saw much more in the Louvre than objects marked with stars in tour guides. On an extremely rainy day it was a good workout to stroll through numerous galleries. You can do a virtual tour through the Louvre.
Paris is not only a classical beauty - we enjoyed some modern parts of it also:

Occasionally I remembered about the street signs and took pictures of them.
Descartes perhaps was honored as a mathematician and as a philosopher, therefore he has two streets. Or may be having several streets named after him stresses how often he used to change his address.

Lagrange is considered alternatively Italiand and French mathematician - Lagrange survived the French Revolution and became the first professor of analysis at the École Polytechnique upon its opening in 1794. Napoleon named Lagrange to the Legion of Honour and made him a Count of the Empire in 1808. He is buried in the Panthéon.

Pierre-Simon Laplace is remembered as one of the greatest scientists of all time, sometimes referred to as a French Newton or Newton of France.

I have to confess. I knew nothing about Maurice Audin who disappeared during The Battle of Algiers in 1957 never having a chance to defend his doctoral thesis. In June 2007, fifty years after her husband's disappearance, Madame Audin wrote to Nicolas Sarkozy, the newly-elected French president, asking him that the mystery of her husband's disappearance be cleared up.

In January 2009, Michèle Audin, the daughter of Maurice Audin, herself a mathematician, publicly declined the French Legion d'Honneur, which had been awarded for her work. As a motivation for her refusal, she cited the lack of response from the French government to her mother's letter.

Another mathematician who suffered because of his political views was Marquis de Condorcet. I have missed rue Condorcet in Paris which is another one named after him like it was with Descartes.

What would be Paris without love? I remeber this song since my childhood.

Maîtresse, embrasse-moi, baise-moi, serre-moi
Maîtresse, embrasse-moi, baise-moi, serre-moi,
Haleine contre haleine, échauffe-moi la vie,
Mille et mille baisers donne-moi je te prie,
Amour veut tout sans nombre, amour n'a point de loi.
(Pierre de Ronsard (1524-1585))

There are more than one ways of saying "I love you". This is a wall where "I love you" is written in 311 languages. There is a video of it here.

More about my trip to Paris next time...

Kinetic art - sculptures in motion

2011-03-09T20:39:00.000-05:00

Kinetic art combines art, engineering and mathematics - I am not sure which of these three components comes first. And there are not only these three - creativity in finding ways to express ideas, making parts... Leonardo da Vinci was reading ancient texts and then sketching ideas of those machines which led him to add his own fantasies. Was he thinking only about practical uses of his machines? Perhaps not, because many ideas we now find in his Notebooks are way ahead of its time. Was he the first kinetic artist?

Art historians are calling Marcel Duchamp to be the first for his Bicycle Wheel in 1913. From MOMA description:
"Bicycle Wheel is Duchamp's first Readymade—class of objects he invented to challenge assumptions about what constitutes a work of art. Here Duchamp chose two mass-produced parts—a bicycle wheel and a kitchen stool—and put them together in an assemblage, creating a sort of nonfunctional machine."

Well, I am not an art historian to judge. My personal experience with geometry needed to create motion started when I got involved in Reuleaux kinemtic model digitization project that eventually grew in large digital library KMODDL. When I found the video about Reuben Margolin making wave sculptures, I remembered my writing on history of linkages which now I wish I could re-do. (I guess I should put it on my "to do" list.)

This is really fascinating. When you watch it, do not miss fast paced place when he does calculations! :-)

It prompted me to find some more kinetic sculptures - like this one in BMW museum:

Joe Gilbertson Kinetic Sculpture:

Teo Jansen and kinetic sculptures:

Arthur Ganson has several videos on his page.
Here are more links to kinetic sculptures, and of course you can search for more.

Geometry, architecture and 3-D printing in fashion design

2011-02-22T20:41:00.001-05:00

Last year it was Poincare Conjecture that inspired Dai Fujiwara to present geometry in his collection in Paris fashion week. This year I am in awe about 3-D printing used in fashion - computers, geometry, architecture - all combined together and applied to create wearable sculptures - not for everyday use of course. Let me just post pictures I collected from the internet of amazing creations by Dutch fashion designer Iris van Herpen (born 1984). From her webpage:

The essence of van Herpen is expressing the character and emotions of an unique  woman and to extend the shape of the feminine body in detail. She mixes craftsmanship- using old and forgotten techniques- with  innovation and materials inspired on the world to come.

Here is a video:

some videos on non-Euclidean geometry

2011-01-12T17:12:00.000-05:00

This post is an answer to those who have asked me - do you have anything on YouTube we can watch? The answer is - no, I do not have anything on YouTube but there are some videos of me available:
this is by Sciencentral Extreme Knitting
then there is in series Mathematics Illuminated Unit 8 Geometries beyond Euclid
the most recent one Talks from the Yarniverse

This time I wanted to point out other video resources about non-Euclidean geometries or related topics.

History of Non-Euclidean Geometry by Jeremy Gray from Open University class:

From the series of Great Courses on You Tube there is a lecture by Prof. Judith Grabiner on the history of non-Euclidean geometry:
part 1

part 2

part 3
in this part I disagree about some of the geometric explanations - but I guess this lecture has been recorded a while ago - straight line is the shortest distance between two points ONLY in Euclidean geometry, also hyperbolic plane IS NOT an extension of saddle surface; etc :

part 4

Amber Case gives her introduction in Hyperbolic Geometry on much lighter note:

Not the Knot should be filed under "movie classics":

make sure not to miss the part 2:

great video on Poincare Conjucture:

most recent one is the talk of Vi Hart at Joint Math Meetings last Saturday in New Orleans:

well, there are more - just search for them online.... :-)

inspirations

2011-01-05T17:02:00.001-05:00

Comment on previous blog entry prompted me to point out some of the wonderful work by others that inspires me. I am not claiming it will be a full list and not in any particular order.
In the very first fiber art exhibit I was invited to participate I saw wonderful sculptures by Blanka Sperkova:

Curator of the exhibit had displayed our works next to each other and on the opening night several people asked me - do you know each other? No, we never met, I wish one day we would.
Then learned about Ruth Asawa:

She had an exhibition I very much wish I saw.
When I see ceramic sculptures by Eva Hild, they always seem to trigger something familiar to me:

In 2006 at Gathering for Gardner I met Brent Collins and later also Carlo Sequin and learned more about their collaboration:

About the same time I met also George Hart.

Lately his sculptures are more with computer aided and 3-D printing possibility inspired touch, which lets to create big collective fun works for all ages. George has such enthusiasm for popularizing art and mathematics - I am eagerly waiting for Museum of Mathematics to open in 2012!
I am very happy to see that George's daughter Vi Hart is know following her father's footsteps with her own creative work. I like her doodles very much

Math inspires artists to create sculptures in different media - I am finding fascinating Desiree Hope glass sculptures inspired by geometric forms:

If I am looking for mathematics and art connections, one of my favorite places is ISAMA page - wealth of information! Online journal on this page Hyperseeing - not to be missed! So do BRIDGES.
Of course, I can go on and on, but enough for now :-).

Happy New Year!

2010-12-30T22:34:00.000-05:00

This is that time of the year when you suddenly realize that only one last day is left for all the things you wanted to accomplish this year.
May be that is even better - to have still things to do on a list. It means that instead of making a new list there will be already "to do" list to keep going!
Thank you for visiting my blog and hope you will come back here next year!

No need to know the area of the rectangle?

2010-12-22T23:49:00.000-05:00

Last time I was in New York I saw an exhibition at New York University's Institute for the Study of the Ancient World about Babylonian mathematics. It is not particularly large but it was very special for me. The first book on the history of mathematics I ever read was a book on mathematics in Ancient Egypt and Babylon by Vygotsky M. Ya. Арифметика и алгебра в древнем мире, 1967

This book was given to me as a present from my beloved math teacher. Since then I was dreaming one day to see these mathematical cuneiform tablets and now finally my dream came true.
These tablets are showing that in Ancient Babylon people knew equivalent of Pythagorean Theorem which nowadays children in US schools first learn in grade 8 according to new Common Core Standards.
Pictorially this theorem is known as:

or we can say that the area of the green square equals the sum of the areas of the blue and red squares.
Too often when I talk about hyperbolic planes people say "oh, I am not good at math". Usually that is said with some regret that they did not have good math teachers at school or were discouraged to be more serious about learning math. I have often wondered - what is wrong with school math? Why it leaves in so many people so bad memories?
There is a saying in Latvian - ' Fish begins to rot at its head." meaning that the source of the problem is at the top not bottom - e.g. we should not blame teachers without first looking how they have been prepared.
Today I heard a shocking quote:
"I got to be a full professor without knowing how to find the area of a rectangle. Why should you expect third graders to learn that?" I think that ANY person should know that but this was not an ordinary person who said that - it was the Dean of Education School of one of NJ colleges.
This story really struck me, so I decided to post it on my blog:

Pat Kenschaft wrote to my husband : "... my spouse was fired last Thursday, allegedly because of an email that I wrote to my list of people who want New Jersey to require preservice elementary school teachers to
take at least one course in mathematics relevant to their teaching. (I'm told on good authority that a dozen NJ deans of education oppose this.Montclair State's said to me, "I got to be a full professor without knowing how to find the area of a rectangle. Why should you expect third graders to learn that?" I have taught areas of rectangles to hundreds of third graders without failure in the sense that they knew it when I left the room.) ".

Here follows the e-mail that had such dramatic consequences:

---------- Forwarded message ----------
Date: Tue, 14 Dec 2010 20:43:48 -0500 (EST)
From: Pat Kenschaft <kenschaft@pegasus.montclair.edu>
To: undisclosed-recipients: ;
Subject: letter to editor re math for elementary school teachers

I had the letter below about the need for elementary school teachers to be taught more mathematics in the "Montclair Times" this past Thursday It is not copyrighted and you are free to use or forward it however you like.
The importance of this issue was emphasized to me recently when a friend reported a conversation with a Monclair second grade teacher. She said she knew plenty of math for her job because the teacher's manual of "Everyday Mathematics" tells her just what she should say each day. She said the children should learn only one way, so there is no need for her to answer probing question or explore their ideas of other methods for solving problems. This, I know, is not in the spirit of those who wrote "Everyday Math," nor is Montclair an impoverished school district. It is exactly the kind of approach that keeps children from growing mathematically. Alas, I fear it is all too typical of American elementary school teachers.
What can be done? I fear that our current governor might use this issue as another reason to undermine teachers, which would mean we would continue to lose our good and experienced teachers. Teaching has always been a challenging career, and now it is losing its advantages with alarming rapidity.
On the other hand, if the state and municipalities really want to improve mathematics education, I believe this is the most crucial step.

Pat
----
To the Editor:

Improving Math Education

After New Jersey's first high school proficiency test was instituted, I noticed a remarkable DROP in the math preparation of my non-majors in college. Test-prep is not education, despite the pressure for AYP.
What to do? Teach the mathematics to elementary school teachers that they are supposed to teach the children! They are capable and eager to learn. They are angry when they realize how much they have been deprived the needed knowledge. Once the children are damaged, it is VERY difficult
to undo when they reach middle or high school. Many again take remedial courses in college.
A national coalition of fifteen mathematics organizations recommends four APPROPRIATE mathematics courses for future elementary school teachers. I know of only two states requiring four, but quite a few require three. New Jersey requires NONE. A reliable source I dare not reveal assures me there are a dozen deans of education in New Jersey adamantly opposing a certification requirement that future elementary school teachers be taught appropriate mathematics.
Concerned citizens can let state officials know of their concern and email me at kenschaft @pegsasus. montclair.edu. They can read about my seven years of helping elementary school teacher mathematically in my paper "Racial Equity Requires Teaching Elementary School Teachers More Mathematics" .
At the beginning of this program I worked with two fine Montclair teachers. Montclair stiffed its teachers, so we didn't contract with Montclair again. Both teachers worked hard anyway. Their students improved greatly, but then one was switched to full-time social studies. We have a new administration now, so Montclair might want to help its elementary school teachers mathematically.
I repeat: the teachers are plenty smart and eager enough! Like the children, they have been let down by our system."

Pat Kenschaft added in today's e-mail:
"This stuff is politically dangerous, but we who do not have a lifetime career to lose any more need to work at it. "(bold/underlining mine -DT)

Art Break in NYC

2010-12-14T22:01:00.000-05:00

yes, indeed, this is that time of the year when people go to New York to see Christmas lights and all what goes with it. I had two days full of art there. First, to the DUMBO in Brooklyn - I went to see Maddy Rosenberg in Central Booking where we chose 9 of my works which will be in the upcoming show. Then my dear friend Gail took me to the Park Avenue Armory to see Peter Greenaway's vision "Leonardo's Last Supper". Peter Greenaway was trained as a painter, so it was really interesting to see what he saw in this painting. The first experience walking in and having a first glimpse of the painting reminded me of the time last year when David and I saw the original in Milan, except there you come in through the door on the right side of the painting. In this performance there is a time in the beginning to take it in as it is. I had another opportunity to check the lines of perspective in this painting, this time avoiding security guards jumping at me and checking what I have in my hand as it happen in Milan - there they thought I am taking forbidden pictures. the look on their faces after I explained that I am mathematician and looking for geometric constructions in the painting was worth the entrance fee...

Next stop - Anselm Kiefer's exhibit " Next Year in Jerusalem".

There is a special border, the border between art and life that often shifts deceptively. Yet, without this border, there is no art. In the process of being produced, art borrows material from life, and the traces of life still shine through the completed work of art. But, at the same time, the distance from life is the essence, the substance of art. And, yet, life has still left its traces. The more scarred the work of art is by the battles waged on the borders between art and life, the more interesting it becomes.
--Anselm Kiefer

Then Gail took me to the two openings - both near Chinatown - it was already dark and I was happy that Gail was leading the way.

When we walked in the first one I saw a guy offering some wine to the guests, he had only one glass left on his try and I thought I should take it. When I took it, I could read in his eyes that he thought I did not deserve it because I am certainly not the one from this crowd. He was right. I found a huge gap in my art appreciation palette. I noticed a tiny sketch of nude, like the ones my classmates in 6th grade where drawing when they first discovered that girls are different from the boys. I thought it was a joke to frame it and put it on a show. I was wrong - these were all donated works and this one had a price....$17,500.....

At that point it was clear that I do not understand this show and it is time to move to the next, several blocks away.

Sorry for forgetting the author's name but he was a handsome man, originally trained as a painter. This place was small but tightly packed with a younger and more democratic crowd than the first place.

Then we returned to Brooklyn to see Gail's own painting.

More of Gail's work is on her webpage. I got to know Gail through her interest in my work, and I am so happy we found each other. I am really thrilled about the unexpected side effect of "hyperbolic crochet" - hundreds of people who did not know each other, get together and connect. One day I will write more about my own experiences, but my friendship with Gail is certainly one of them. Some times I never meet people but we have only e-mail contact. Like it was with Cat Bordhi - she has wonderful knitting books with a mathematical twist. Marie-Christine Bevington came to my talk in Kitchen (February 5, 2005). She told me that she was surprised to find out then that she was making hats with some hyperbolic crochet in them. That talk inspired her to further explore the possibilities and she came up with many more interesting hats. On Friday I had a chance to see all these hats.

This hat is Christine's original design - made of hexagons, pentagons, squares, and triangles. This hat snugs any head really nicely due to positive curvature formed.

All these different hats were fiber art objects on their own right. Thanks, Christine, for inviting me!

I visited also Cooper-Hewitt museum to see the National Design Triennale, and of course, The Bleached Reef in it.

How about the Christmas lights? Well, did catch some just before the bus back to Ithaca.

news

2010-12-04T22:56:00.000-05:00

First - this is a reason for not posting:

It is not all new - this is the same large pink hyperbolic plane made of 88 skeins of yarn seen in my book with a cat. Now it is 20 skeins larger (I found some leftover stock of discontinued yarn on eBay). It actually is just two more rows added but with more defined outer edge and some support and now it measures 30 x 30 x 22 in and weighs about 6 kg.

Hyperbolic Crochet Coral Reef is featured in today's National Geographic News blog - look for a video and nice pictures from the exhibit in Museum of Natural History in Washington, DC.

Geometry continues its presence in high fashion

2010-11-29T12:51:00.000-05:00

In the autumn of 2010, ISSEY MIYAKE’s Reality Lab. is presenting “132 5. ISSEY MIYAKE”. Reality Lab. is a research and development team lead by Issey Miyake and two staff members, Manabu Kikuchi (textile engineer) and Sachiko Yamamoto (pattern engineer) and comprised of a group of designers, some of whom are young and relatively new to the Miyake Design Studio. The Reality Lab’.s team first met computer scientist Jun Mitani (Associate Professor at the Graduate School of System and Information Engineering, University of Tsukuba) who is specialized in form modeling in computer graphics and were introduced to his unique geometric shapes in 2008. Inspired by CG application* developed by Dr. Mitani that creates three-dimensional paper model with smoothly curved surface out of a single flat sheet of paper, the team embarked upon a new adventure in research.

The name, 132 5. was born from the above-mentioned process. Each of the numerals has a special significance. The numeral “1” refers to a single piece of cloth, while “3” refers to its three-dimensional shape. The following “2” comes from the fact that a 3D piece of material is folded into a two-dimensional shape, and the “5” separated by a single space refers to the time between when the folded forms are made and people actually put them on, giving birth to clothing. The numeral “5” also signifies our hope that this idea will have many other permutations.

More about it here.
and a nice interview

Where I grew up

2010-10-29T17:31:00.001-04:00

I arrived in Riga from Washington to find the snow which melted in couple hours letting still to enjoy colors of autumn leaves. So far it has mostly been raining (or wet snow) with some wonderful exceptions of bright sunshine, allowing me to take some pictures of my native city.

Riga does not have a central plaza. In 1990 part of the street near The Freedom Monument was closed to traffic and that made a central plaza for public gatherings.

The Freedom Monument is dedicated to "Fatherland and Freedom", erected 1935 (author K. Zale) it is 42 m high and has a nickname Milda for a woman holding three stars that represent three parts of Latvia. During Soviet times this monument was considered for demolition but the prominent Soviet sculptor Vera Mukhina, who was born in Riga and was a student of K. Zale, is credited for saving it.

These houses in Old Riga were built against the medieval city wall.

This is one of the favourite spots for postcard pictures and paintings of Old Riga

Part of old city wall which at some point was nicely restored but now is "getting old" again

I love to walk in Old Riga to find houses nicely restored.

It is clear that tourist season is over, also some of my favourite places on this street has disappeared due to current economic crisis.

This is the house where my family lived until 1961.There has always been a store on the first floor. This was the first store in my life where I did shopping - my parents sent me down to buy a bottle milk which I proudly bought and was carrying back but dropped on a door step and the glass bottle broke. I guess this unfortunate first experience with shopping left lasting impact on me - I still do not like shopping. There is an earlier story about me and this grocery store. The most expensive sweets there were truffles wrapped in golden paper like a little parcels.I never was a big candy lover, but that one time I decided that I must have a truffle. I had seen adults at neighbour's party eating them with after dinner coffee. I was about 2 or 3 years old at that time. Nobody would allow me to taste coffee (anyway, I knew from some left over drops in cups and glasses that it was bitter and the liqueur with it was just awful). But truffles were something I had not tried and one time I decided not to leave the store until I got one. When my mother had paid for her groceries and continued to ignore my requests for a truffle and instead pulling me by the hand out of the store, I decided to stay there and screamed as loud as I could, "Iwant those truffles!". At least it was what I thought I insisted. I did not know how to pronounce that fancy French name correctly, and there is a Latvian word in folklore not suitable for use in literary language or by a child. My mother blushed and tried to get me out of the store - that of course made me more determined then ever. The ladies in the store were laughing until they cried, and they gave me a truffle. Was it so special as I expected? No, it had a lot of pure cocoa powder around it, and it was a little bitter too. There came a lesson that if you can not get something, maybe it is even not worth longing for it. By the way, I like only bitter chocolate now.

This is the courtyard of the house we lived. Windows of our room were 2nd and 3rd from left on third floor - the first one which is not in line with others is a window on stairwell. Next two narrow ones are from so called "maid's room", that was used as a pantry for everybody in the appartment. Next one is kitchen window with a little opening on right side that was for "a cold cabinet" - there were no refrigerators in the appartment. We lived in this appartment together with other people. There was an elderly couple who once owned the whole building but now had only two rooms left for them. It is a mystery to me how they managed to escape "a free trip to Siberia" in 1940 when mass deportations from Baltic States took place. In one of the rooms there was a single woman, director of bread factory. She used to bring occasional pastries for me. Two other rooms were for Professor's family. Prof. Skuja (1886-1983) was a very special person to me. He was my first teacher - taught me to read at the age of 4, taught me that the most valuable thing one can possess is knowledge. He said: "Everything else can be taken away from you, but what is in your head will always be with you and will help you to survive." He knew what he was talking about - he was a doctor and professor but for political reasons had a knowledge of cells in KGB, after 1950 was banned from teaching and forced to retire. He was working on Latin-Latvian-Russian dictionary of medical terms but it was published as "the lifetime work" of somebody else (K. Rudzītis. Terminologia medica in duobus voluminibus („Latīņu-krievu-latviešu medicīnas terminu vārdnīca divos sējumos”). - R. Liesma, 1973. - vol 1 -1039 pages, 1977. - vol.2 - 866 pages. Those little index cards for the dictionary are very vivid in my memory - I was not allowed even to blow on them. I saw how much time he spent on this work. I do not know the details of the agreement to do the work that will be published by somebody else, but this was my first experience when intellectual property laws were violated, and the feeling of unjustice has stayed with me ever since making me very sensitive to these issues. I could not know at that time that my own work will be published as somebody else's research.
Professor was often my babysitter. We had an agreement that if I let him finish what he had planned for the day, I could sit in his lap and we would go through books together. He taught me anatomy by the age of six and lots of interesting things. He taught me to play chess but I never became too fond of it, I liked checkers much better. Because of him I always wanted to be the best student..We already had moved out of this place when I started to go to school but at the end of each school semester I would come to visit him to show my report card.

All other rooms inn the appartment had windows on a street side with sun coming in, our room was originally a hallway for the appartment, so this was scene I remember looking out of the window being left home alone when I was sick and my parents had to go to work. There were no cars at that time and walls were grey and dirty because of smoke - there was no central heat, we had wood stoves, and my father was carrying wood up to our appartment from a storage place which was in the other courtyard through the gate in corner.

Sometimes I would be let to go out on my own in the courtyard and then I would violate the rule not to go to the street because there was another door leading to the grey building next to ours, and I would come out on street through it, walk around the corner and come back to the courtyard. I was scared to be alone on a street but I pushed myself to do it in order to build my selfconfidence that I can do it.

This fenced parking lot used to be a little neighbourhood park with a sandbox and benches around it. This was very close to our place so I would be there often with some of the adults who would chat or read newspapers while I was playing with other children.

To prolong my time outside I was walking back asking questions about the buildings on our way like on this one next to the little park. I was curious about the people living there - who are they, how their appartments look like. I visited tis house couple times when I was in middle school - one of my classmates lived there.

This was the way back home - downhill one block.

I always was fascinated with this corner house

and its continuation on a little side street.

Across from it in the basement/ground floor of this red building was my first "restaurant" - it was a pancake place which was the first place I remember where waitress would come at the table and ask what kind of pancakes would I like. And then we had to wait some time until pancakes would arrive piping hot and crisp with jam and sour cream.

Those two modern buildings are bult on place of two story wood buildings across the street from ours.

This is the next street corner.

Across from the building above is this three story building which was the newly built furniture store where my mother worked. I liked to go there because they had whole rooms on display and they were so different from the one we lived in. But mostly I liked to sit on the windowseels while waiting for my mother and watch the street. That was so much more fun than looking out the window of our room.

That two story building - I am amazed it still exists - was my day care center. It was just a block away from our appartment, therefore convinient, but it was for Russian speaking children. So I learned Russian very early. Unfortunately my language learning was not very consistent because I was sick a lot.

This is me in 1957 and the day care place is behind me. The next picture was taken in March 1957 and is still my most favorite of me:-)

Turning on the same corner to the other direction I was taken for a longer walk - usually towards the church you can see at the end of the street.

This was a modern building I guess in 30-ies and still counted as modern and fancy in 50-ies. Pancake place I mentioned before is at the other end of this little street.

I was very happy to see that bending houses around the church are nicely restored.

On the way back from a walk around the church if I was lucky we would stop in shop that was in the building you see in the middle. There were candies plain and fancy, cookies, halva several different kind, pastries, cakes... I would get something very simple but I liked to see that all as a symbol of the life in different world - of the world for people who could eat whatever they desire, who were wearing fancy outfits and would not notice me.

Riga is famous for its Jugendstyle (Art Nouveau) buildings. This one is particularly important as an example of national romanticism at the beginning of 20th century (architect Eizens Laube).

Couple more pictures from the same area for my friends who wanted to see the architecture in Riga.

Strongly Connected Components Episode 23: Daina Taimina

2010-10-26T08:41:00.001-04:00

I am in Riga, Latvia, enjoying some sunshine after rain, rain, rain....This morning I walked on a street where I grew up and will post pictures next time, but for now you can listen me talking with Samuel Hansen

Strongly Connected Components Episode 23: Daina Taimina

Hyperbolic Crochet Coral Reef in Smithsonian

2010-10-20T18:13:00.000-04:00

In Ithaca geese were getting ready to fly away, so do I - first toWashington, DC, then to Latvia.
Sorry for beeing late posting photos - I was attending VIP event of opening Hyperbolic Crochet Coral Reef exhibit in Smithsonian Museum of Natural Historyon October14th on my way to Latvia where I am now for a month. The exhibit looks great - first thing you walk in is huge Smithsonian Community Reef which is displayed ver well. Other parts are placed around it and I am sure will be of great interest for visitors to explore.
studio360 had a nice piece on this event: Crochet, Geometry and Coral Reef

Benoit Mandelbrot (1924-2010) has joined fractals

2010-10-18T17:34:00.001-04:00

It is always sad when you travel, did not check any news for some days and then learn that some great person has died. It feels to me that Benoit Mandelbrot has joined his fractals - his ideas will keep dividing and spreading and making new appearances.
obituary in NY Times
and great interview with Paola Antonelli
Beauty from Anarchy - Mathew Santhosh in The Huffington Post
pictures from BBC News

Hyperbolic Guitar and some new photos

2010-09-21T20:40:00.014-04:00

Now there is "hyperbolic music". I was very delighted to learn about this piece, hope you will enjoy it too. While listening to it, look at some my new photos.

Donal Donohoe says about creating this music:
The piece is an attempt to capture the exponential expanse of hyperbolic space in the rhythm of music. Exploring the relationship between hyperbolic geometry and music, this tune was composed after attending a lecture about hyperbolic geometry by Dr. Daina Taimina at the Science Gallery, Trinity College Dublin.
More explanation is on his blog
Hyperbolic Guitar on YouTube

Talking and writing about math

2010-09-20T11:33:00.000-04:00

Recently I met Gabby - Gabriele Mayer was visiting Ithaca several weeks ago and showed me how my hyperbolic planes have inspired her. I am really fascinated with her work (or may be proud that I could inspire something like this?or both? :-) ). Just look:

and here is more on her webpage.

In turn, she inspired me to do something like that to my own work and here is a result:

I am waiting for leaves to turn more in fall colors to take pictures of few other pieces I finished.

With Gabbi we were discussing not only about crocheting hyperbolic surfaces but also how to talk and teach mathematics to students who have "math phobia". We both had an experience that these crocheted surfaces somehow open up people, may be it is crochet as a medium which makes math more tactile and less scary.

Still there are mathematicians who think that not anybody can understand deep ideas therefore there is no use to talk to somebody outside mathematics about these ideas, and there are science communicators who are trying to explain mathematics accessibly but doing it through oversimplifying and as a result perpetuating misunderstandings or simply making mistakes. Some say - it does not matter what are you saying to general audience, they will not understand anyway and they don't care. I disagree with both extremes. When I am talking about mathematics, I do it with a great respect to my audience and it does not matter whether they are people in local library, yarn store, children of various ages in Exploratorium or fiber art enthusiasts on MIT campus. It is much easier to talk to professionals in your field than to people who are unfamiliar or have very little previous experience with what you are talking about. In case of mathematics - had experience but often unfortunately it has been bad. And it has been bad because they had teachers who thought if you cannot follow me you do not have math aptitude or skills and I am not waisting my time to try to explain all that math to you - you won't get it anyway. I am happy that people come to my talks not only to see these various crocheted forms but also to learn what is behind them.

Last Monday Steve Strogatz was talking about "How to write for New York Times". It was about his experience of writing 15 columns about mathematics for New York Times web version. They became very popular. Harvard Business Review called him "the best NYTimes business columnist you never heard of".

Since the talk was in physics seminar (well, I was finding it as a significant fact...), Steve Strogatz invited everybody to be in "full physics mood" - to ask questions, actively participate in discussion and he was asking a lot of questions to the audience. His first questions to the audience were - what would you do in my place if you would be offered to write these columns? How to choose about what to write? To whom you would write? Somebody said - to people who read NYTimes. But who are these people? They are intelligent, most of them well educated, know a lot(or think so since they read NYTimes:-)). One could write towards students - Strogatz remembered nice question one kid had asked him about infinity - is it odd or even? Somebody in audience said ( I did not see who but had to be a mathematician):"to make them like us". Somebody suggested (also a mathematician, this time I did see):"We have to explain accessibly mathematics to all our students in order to influence future voters - they will become ones who will vote to give or not money for our research." Very good pragmatic point.

Strogatz added himself - I could wrote for skeptics to show the point of mathematics and then quieter added - if there is any, which made audience to laugh. He decided to write these columns as for his friend who is an artist and loves math and wants to understand it but has gaps in his knowledge. He choose to follow advice from famous mathematician who at some point was teaching in Cornell Mark Kac:

"In teaching math you should tell truth and nothing but the truth, but not the whole truth."

I think it is a very good advice to follow - to tell truth, even if you are talking about mathematics :-). And if there is something which is too hard for the audience - be honest and tell the truth. I am not afraid to say - I do not know. Because I know that there are more things that I do not know than those I do know.

I mentioned my talk in MIT. It was a nice trip to Boston - I planned so that at least finally I could be also a tourist there! My talk was in famous Stata building. There are many nice pictures on web of it but here are some of mine:

My talk was in the auditorium 123 which somebody told me is the nicest room in MIT - I was very happy about that. The auditorium has 300 seats which I was not expecting to be filled on Friday evening but there were definitely less empty spaces than I thought. The first thing I noticed walking into this room was very professional - so much blackboard space....And screen when you want to use a computer projector does not cover writing space. Since we were driving to Boston I could take with me a lot of models - I am trying to avoid carrying models on airplanes in checked baggage after once my bag with models was lost for 3 days. You may notice in one corner that I put out crocheted shawl - since this was a group of mostly knitters I wanted to demonstrate that I can crochet not only hyperbolic shapes and I am wearing a vest I made.

I liked the audience during my talk very much but it is always my favorite time when after the talk all come to see and to touch and to talk with me.

I do not mind for somebody to find new applications of my work.

I had a special interest in Cambridge - to go to Peabody Museum and to find the sailing maps or navigation charts of Western Pacific made by native people.

In the same hall I really enjoyed various patterns on crafts - I am collecting pictures of patterns in various cultures for my rpoject to write about them:

Peabody Museum is connected with the Museum of Natural History which would be very interesting to see but we were running out of the time - we visited Harvard campus before my talk. Still I decided to give up plan to rest in my comfortable hotel room before a talk in order not to miss the glass flowers collection.

The collection represents more than 830 species all made of glass...It is really beautiful.

Some of my tourist's images of Boston:

We were lucky to have a perfect day to see Hancock Tower exactly how it was designed to see it.

On Copley Square one place not to miss is this:

Isn't it make you think you are in some palace in Italy? Would be very nice to spend some time in it and people do

Indeed Boston Public Library looks like a palace and I was glad to see that there were quite a number of people using a large Reading Room on Saturday afternoon.

The trip to Boston was great but there is always some inevitable disappointment. This time it was here:

I have spent enough time earlier in my life lining up for bread, butter, meat,.... Out of habit to do it now, so this pastry shop thought voted #1 in whole country will have to wait for me. May be it was exactly what I needed for my health - lots of walking and no pastries?

talking with Patty from Lion Brand Yarn Studio

2010-09-19T23:51:00.000-04:00

architectural academic crochet

2010-08-28T23:57:00.000-04:00

This is one of my recent projects. Just to show that I can crochet something else, not just hyperbolic planes. Since there is a crochet in the title of my blog I should write about it too. Especially because recently one of my friends complained that my blog is too academic, too mathematical, and too serious. I think he meant too boring, just was polite not to say that to me directly. May be he is right, I am too serious. But it is hard not to be serious when you live near the big and serious university and go to the talks that are serious. Just going to these talks mean that you are serious, especially when you go to the symposium early Saturday morning like today.
Yesterday and today there was a symposium Shaping Architects=Shaping Architecture in Cornell.
I am finding it quite fascinating to listen talks in the areas with which I am not very familiar. Architecture for me associates with buildings - I was fascinated by Newgrange built 5,000 years ago on my trip to Ireland; last week I was equally enjoying walking around San Francisco looking at the different patterns used for exterior decoration of Victorian houses and I was fascinated by modern buildings in Financial District. I have read some history of architecture but it was about different styles, not about how architects get their ideas, how do they think, how do they explore space, and how do they teach their students. This morning I had an opportunity to peak in the kitchen of architects because they were exactly discussing how they teach students design ideas.
Discussion started with an introduction by Prof. Dagmar Richter about the history of teaching architects. First Academies or Schools of Architecture were created in 16th century Florence and France. It was decided then that architects are more noble than craftsmen that were organized by guilds. There is some parallel here with mathematics in Ancient Greece when theory was separated from practice - mathematicians were supposed to think about ideas but calculations had to be left for specially trained slaves. In 16th century architects were supposed to create art for aristocrats. It was defined that architects should stop doing things by their hands but only create ideas. Politically these first architecture schools were against democracy. No wonder they were destroyed during the French Revolution and new type of schools was created - schools that prepared architects for building military objects and state buildings. That has historically created two directions in architecture which are still fighting, and currently architects are trying to understand where architecture is now.
My particular interest was about the talk by Gisela Baurmann Crocheting Algorithms.

In Gisela's design studio students use crochet as a conceptual model of fabrications and then form there move to digital models. In her talk she was exploring similarities of crochet and patterns in nature on different scales - in visible dimensions and on a cell level:

When only contours are left these patterns from nature become look like a fabric.

When ideas are developed further they start to turn into design.

There are more pictures on her studio blog. Fascinating pictures to foster design ideas can be seen also on Jonas Coersmeir's studio blog.

So - sorry my friend - when I was concentrating on hyperbolic part of my blog title, it was too mathematical=academic. I tried this time to concentrate on crochet part but it turned out also to be academic. Still I hope that not everything academic is boring - at least for me it was fascinating to learn that crochet can be academic....

There are more fascinating projects by Gisela Baurmann and Jonas Coersmeier here.

Lessons from another million dollar prize

2010-08-27T01:00:00.000-04:00

I do remember that on October 2, 2006 Netflix announced a million dollar prize for improving their algorithm used to suggest movies based on the previous rankings by the viewer or mathematically speaking it meant to have Root Mean Squared Error drop by 10% (or Mean Squared Error by 19%). If nobody comes up with this result, Netflix promised $50,000 for the best result each year. I have to confess that I was hoping that somebody will come up with a better algorithm in a year. But I did not hear anything after a year. Somehow I had missed the news last September about announcing winners of this million dollar prize. So I was really happy to notice in the first seminar bulletin of the new academic year that today Robert Bell from AT&T labs-Research will be talking about this Netflix Prize.

In the beginning there were 50,051 contestants for the prize. It was interesting to learn about the amount of data and parameters of this problem and also that solutions were searched not by individuals but by teams. The whole process was a long and dramatic marathon that ended with a photo finish. First all teams were given training data - it means 100 million ratings over 6 years (2000-2005) by 480,000 users for 17,700 movies (movies here included also TV shows etc.). Then there were test data - last few ratings of each user. Robert Bell gave some interesting details about these ratings - for example, in 2004 people became happier - the movie ratings became higher, why - it is not clear, as he put it - it does not mean that Hollywood became better. Data were scattered - some people rated only movies they liked or did not like, some rated every movie they watched, some rated only occasionally. There were also some extreme cases - one user had rated 17,651 movies (almost every single one) with average rating 1.9 (on a scale form 1 to 5), the other rated 17, 32 with average rating 1.81. One user managed to rate 5000 movies in one day - as Bob Bell commented - that user must have had some computer science background to do so. For unknown reason the most rated movie appeared to be Miss Congeniality. Average number of ratings per user was 208. Huge amount of data, nevertheless 99% of data were missing and certainly not missing at random. Users were identified just by their ID number. It means that if some user did not rate any children's movie, you can assume that this user is not a child. It became clear that what you rate and what don't provides info about your preferences. User behavior may change over the time.
The research team came up with various models - largest one took about a month to create and consisted of billions of parameters.

Statistician G. Box : All models are wrong; some of them are useful.
When solving such large problems it is important to find good teammates. In the process of the competition some teams combined together, some invited helpers. First year Bell's team had 107 sets (methods), at the end the number was over 800. But one of the lessons they learned was that a handful of simple models achieve 80% of improvement.
The race at the final days of the competition was very very close - when it was 11 days left to go first three teams had results 9.91%; 9.89% and 9.83%. The two leading teams had the same result but the winner was the team who submitted their result 20 minutes earlier...
At the end of course there is a question - how about the money? Robert Bell said that the million dollars initially were important to attract researchers to the problem, later somehow the money issue lost significance. It was the challenge to solve this multi-layered large data problem that kept researchers going. There were interesting ideas appearing during this competition, lots of collaborative work.
Who received million dollars? Well, look here.
More about how this Netflix prize was won.

Hope and Disappointment

2010-08-18T22:50:00.000-04:00

I was busy - last Thursday I gave a talk in Lion Brand Studio in New York. My friends gently warned me beforehand that I should not take it personally if there will be not so many people because in August everybody leaves New York. I was really surprised that house was full- some people even made it to the talk from Washington DC!
In my stories how my crochet sculptures come along I was telling a story about a dream - in my dream I was crocheting a huge hyperbolic plane, so huge that I could not move my fingers anymore and suddenly it occurred to me that if I could figure out how to do the next move I could solve P versus NP problem. Of course, I woke up before I solved it.... The feeling after was very strange - I never attempted to try anything with this most famous computer science problem. Yes, my graduate work was in Theoretical Computer Science but it was so long ago that seems - it was in my previous life. Then I did not know whether there is any connection between hyperbolic planes and P v.Np problem. This strange dream prompted me to do some research and I learned about Margenstern's and Morita's paper NP problems are tractable in the space of cellular automata in the hyperbolic plane.(Theoretical Computer Science
Volume 259, Issues 1-2, 28 May 2001, Pages 99-128)

They solved the problem on a particular grid that is possible only in hyperbolic plane - it is rectangular grid but made from pentagons. I had to make this grid and this is how this illustration was created:

Very distant touch to the famous problem! I first learned about this problem when I started my work in Theoretical Computer Science. My thesis advisor Prof. Rusins Freivalds proudly showed me a guest book where Juris Hartmanis while visiting University of Latvia had written: " Call me anytime if you solve P versus NP". Of course my question then was - what is this problem?

I already wrote about one of Clay Institute prize problems - Poincare conjucture that was finally announced to be solved. P v NP is another "Million dollar Prize" problem. (The definition of the problem is a question whether P is equal to NP; P being the set of problems that could be solved in a fixed amount of time and NP being the set of problems whose answers could be verified. ) But it is not about who will get million dollars - it is about the understanding why I was hoping that one day somebody will solve it. It is one of the deepest questions ever asked. I do not want to claim that I can perfectly explain what it is about but here is an explanation: P vs. NP for Dummies. This problem has long history of being a conflict point between mathematicians and computer scientists. Not the only one, have to admit from my experience. I think it comes from different ways of thinking about problems and deciding what is most important.

And now comes an explanation of the title of this blog - Hope and Disappointment - it was last week when headlines in news were saying P vs NP problem solved - but carefully posting a question mark at the end or

New proof unlocks answer to the P versus NP problem—maybe or Has the Devilish Math Problem “P vs NP” Finally Been Solved?

Vinay Deolalikar on August 6th announced that he has proved P is not equal NP. If you search Wikipedia for his name you will be redirected to the page about the problem. From a cached copy I learned that
"Vinay Deolalikar was born in New Delhi, India. He completed his masters in electrical engineering at the Indian Institute of Technology Bombay in July 1994, and obtained his Ph.D. from the University of Southern California in May 1999."

It is a challenge now to understand his proof and for him to fix flaws what others are finding in this proof. As Forbes blog say: Now, It's the Slow Roasting of an HP Mathematician

Scott Aaronson in his blog is giving Eight Signs a Claimed Proof is Wrong.

It is not clear is this proof correct or wrong but it is as far as I know the first serious claim of proving this problem. Such problems people attempt quietly - how many others are working on this problem? Nobody eally knows. Will they come out with their ideas now? We will see.

I was following some of these exciting (some icy, some heated) discussions with a delay because I was in New York after a long absence and really enjoyed seeing exhibits in MOMA - Matisse, which is very crowded and no photos, of course. But there is another one - works of Lee Bontecou: All Freedom in Every Sense which I liked very much:

I visited some of my favorite paintings in MoMA, walked in Picasso exhibit - Themes and Variations - it is interesting to see his protraits of wives and lovers which reflect how he was feeling about these women. I wish there would be a drawings next to them by these women how they felt about Picasso - just for the fairness...

When I reached this:

I decided that my understanding of the modern art has ended and I have to move to other place.

There was a great exhibit in Metropolitan museum - I am glad I had a chance to see it - American Woman: Fashioning a National Identity In the morning on NPR I heard Susan Stamberg talking about it and later it was really nice to see it myself. Next to it was another, much quieter exhibit Italian Drawings - I was thinking - I wish I could draw like that... Both of these exhibits were right next to Impressionists -

Then Turner

And then the painting tyhat really struck me:

It is the painting by Arkhip Kuindzhi - I did not know that his painting was in Met, may be it was on loan when I was there before.

It is worthwhile to get to the Met's roof - of course, the view is great, but right now there is bamboo construction by Doug and Mike Starn.

When in New York I always try to go to some place which I like very much and some place where I have not seen before - it is a reason I love New York - there are always such places! This time I walked on The High Line - it is a city park built 2.33km built on a former freight railroad on Manhattan's West Side between 20th and 14th street

It would be nice after the walk to disappear in Chelsea Market, particularly because it started to rain. Unfortunately, my time was over and I had to catch a bus.

So my hope for the P vs. NP problem is that one day someday will really understand it, may be it will be Daolalikar, my disappointment is about some mathematicians being arrogant and icy about his attempt - may be it is jealousy or may be they are acting like traditional mathematicians usually do...

My hope for New York was, of course, to do more, my disappointment - some people really leave New York in August and I missed meeting them... Well, there will be other times...

College mathematics or math about college

2010-07-30T10:28:00.000-04:00

The other day mail came with the most expensive DVD we have ever purchased. I'll better will not add up because it has not been paid all at once, but it is many thousands of dollars. Have you guessed what it is?
DVD of my daughter's commencement.

It brought back some of my thoughts from the time when I was full time teaching 120 students. Each student means around $3500-$4000 paid tuition per course. You think I had a fantastic salary? I cannot blame you for this misconception if your answer is yes.

If you are not a contingent college professor then your image of college professors may be is made up by movies - like a classical one "My Fair Lady" - have you noticed all the staff Professor Higgins had at home?

"My Fair Lady" is my favorite movie but my salary was nothing compared to Prof. Higgins means or any other more recent movies depicting college professors in fashionable home interiors (for example,"Chloe").
In reality my salary for teaching 120 students (do math yourself how much tuition it is) was not enough to cover the tuition for that same semester for one of my children but I had two in college... I felt that something is wrong, very wrong. I am not complaining here that my salary was low (there are many colleges that pay even less per course to contingent faculty), but I thought and think that tuition in American colleges is way too high. If my teaching a class is a product and that is sold to students for 10 times more - the question arises - why are the universities called non-profit organizations?

I am not alone in my feelings. In a recent public survey report by Squeeze Play 65% of respondents are saying that higher education are rising at a faster rate compared with other things and 74% of them say that this rate is the same or even higher than that of health care costs. In a recent issue of Academe (July-August 2010) If the costs are rising so rapidly, there should be raised question about the quality of the product that has been sold for such a high price. The whole issue of the current issue of Academe is called "What do faculty owe students?". There is an interesting article by Peter Sacks where he talks that "access to higher education is not determined simply by one's ability to pay for college.Some children are born on the right side of the class divide ...Despite what we may believe about our higher education system's role as a great equalizer for social and economic mobility in the United States, we have created a highly structured system of colleges and universities that, more often than not, actually perpetuates inequality."
May be it would be smart to skip the college? This is one of the questions Rebecca Mead raises in New Yorker because odds of getting job (any job) for class 2010 are lower now than one imagined four years ago. Are colleges responsible for preparing students with degrees that are useless? Why not - parents have paid thousands of dollars or students have taken student loans that have to be paid (even in case a person dies, then this loan passes to the next of kin!!).
There is an interesting discussion about the real cost of college textbooks which also talks about financial burden of college education.When I searched Google for college affordability first jumped out this report - it is from 2003! What has changed except prices are even higher?

Is all what is left is to console ourselves with this Your new college graduate - parents guide?

The story about the origins of the model of hyperbolic plane

2010-07-24T23:43:00.005-04:00

This is something I really wanted to get to the very roots but did not get a chance to do when writing my book Crocheting Adventures with Hyperbolic Planes. It is about the very first model(s) of the hyperbolic plane. When I crocheted my very first hyperbolic plane in 1997 I knew about the existence of paper models and the idea was attributed to Bill Thurston.

I knew also that the very first model was done by Eugenio Beltrami in 1868 but I could not find anything more at that time except that he made a pseudosphere. Later I took a picture of a plaster model which was on an exhibit in Kettle's Yard Gallery, Cambridge University, UK, but it was not an original one. I even did not know whether original Beltrami models still existed!
On July 13 David and I received a message from Italian mathematician and historian of mathematics Piergiorgio Odifreddi who draw our attention to online document by Maurizio Cornalba pointing to the page 15 with pictures of original Beltrami models and asking a question whether this is the same idea as Thurston's.

I did not know the answer and I always was curious how Bill came up with this idea, so I finally asked him this question. Here what Bill told me:

"I don't recall having seen Beltrami's paper models, although I was aware that Beltrami had shown that the pseudosphere had the intrinsic geometry of the hyperbolic plane. At New College (he graduated from it in 1967 - DT), a handful of math majors held a "senior seminar" in geometry --- purely students --- and we went through large portions of Coxeter's Geometry book. I looked at a few other books about geometry and hyperbolic geometry that were available in the library, but I didn't know very much. I was struggling to get a grip on what the hyperbolic plane looked like, so I started piecing it together in an obvious way (while also doing it for a sphere, for guidance) using concentric circles with shape gotten using trigonometry, length 2 pi sinh(r) and curvature cosh(r)/sinh(r), (radius 2 pi sin(r) and curvature cos(r)/sinh(r) for the sphere). Soon it became obvious that the shapes in the hyperbolic case were converging, so I switched over to using congruent annuli. I was trying to model the hyperbolic plane, not the pseudosphere picture --- but of course it was soon obvious that you could wrap the construction around a pseudosphere. It seems like the kind of thing that could easily have been rediscovered many times. Also, I think people have probably made models for the pseudosphere in lots of ways."

Here we go - my first correction - I have been saying that Thurston came up with this idea in 1970's but actually he made his first model while still in college! He graduated from college in 1967, that is when I finished 6th grade and had received my first prize in mathematics - Martin Gardner's book (I added a picture of it in my blog about Gardner.)

This is the picture of the courtyard in the University of Pavia. Eugenio Beltrami started to study mathematics here in 1853 but was expelled in 1856 because of his political opinions according to Wikipedia but according to Mac Tutor biography - he had to stop his studies because of financial hardship and had to take a job...(hmm -  which on of those reasons? or they both go together?). In 1868 when making his hyperbolic plane model Beltrami was a professor of mathematics in Bologna. It had to be important to him  to take his paper models with him when Beltrami returned to University of Pavia 1876 and taught there for next 15 years. These models are now in the Department of Mathematics of the University of Pavia.

Prof. Odifredi, who is currently writing a book in history of mathematics, contacted Prof. Cornalba and sent us pictures of the original models, the very first models of the hyperbolic plane, made by Eugenio Beltrami.

I was really excited seeing these pictures - here they are - the very first models of the hyperbolic plane! I am excited not only as somebody who has taught for many years and loves history of mathematics. My excitement is also for very personal reasons.  I never liked the lines in media once mistakingly put up there and then repeated many times over and over again, against all my wishes - that is a line about this "superwoman who made a first model of hyperbolic plane which men could not do for hundreds of years. I had tried to correct this misquoting many times, only few times I succeeded.

Thank you Prof. Odifredi and Prof. Cornalba for sending these pictures to me! Thank you also for Beltrami letters to another Italian mathematician Luigi Cremona where he was discussing pseudosphere and why it is a model of the hyperbolic plane.

Odifredi kindly translated some passages from the letter:

"the model is a circular piece of a pseudosphere... the surface is bent into the form a surface of revolution, described by equation n. 16 of my paper of 1868, and its meridien is a transcendent curve, whose equation cannot be given in finite terms. its minimum parallel is one of the diameters of the bent circle: it could also be any geodesic chord, but then the surface would not be symmetrical on both sides" then he says that a few lines are marked, corresponding to some "diameters" and some "horocycles, who, despite having the center at infinity, have a very strong curvature: actually, they're made of little paper arcs with a radius of 25 centimeters, which is the same as the radius of the surface. The total perimeter is more than 6 meters, and its geodesic circumference is made of little paper arcs with a radius of 24 centimeters each". he also says that he was thinking of writing a paper to accompany the model, but apparently he never did. and he adds that he add "some ideas about how to make a better model, with different means and materials". so, the model is actually a piece of pseudosphere, but it's not clear whether he thought that it could be extended to the whole hyperbolic plane. however, beltrami got his two models (the so called Klein and Poincare' models) by extending to the whole circle the geometry of the horocycle corresponding to the pseudosphere."

At the end, of course, there was a question now for all of us: "after all this, what do you think? is it the same model as Thurston's, or is it something different?" Who else than Bill Thurston himself can answer this question:

"The photos look like they're constructed differently, from the region the graph of e^x and e^-x up to some scaling choice on the x and y axes, but the description sounds like it's exactly the same construction with annuli. I wonder if the paper models that Beltrami sent to Cremona are different? In any case, from the translation, it seems clear Beltrami had the idea."

Pictures of Beltrami model and his letter are used here with the kind permission of the Department of Mathematics, University of Pavia. Prof. Odifredi's forthcoming book (volume 1) will be in Italian, in English you can read his book (with a foreword by Freeman Dyson):
The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

This story once more reminded me about the importance of finding the origins of the ideas, going back to the original sources instead of quoting somebody who heard it from somebody else etc.