Sunday, May 23, 2010

Remembering Martin Gardner

When I first won math competition - it was in middle school - my math teacher gave me a small paperback, printed on cheap paper but with an amazing content - it was translation in Latvian of one of early Martin Gardner's books. It was in 1966. I never met Martin Gardner in person but I feel I have known him since then. It is for 43 years.
When I learned that he died yesterday, I had a feeling that I have lost one of my teachers. Gardner's books made me to realize that mathematics can be a fun. that there are much more in math than piles of algebraic formulas we had to memorize (I was lucky - it was easy for me!), I learned how to do some tricks with cards and other objects and learned about mathematics behind them. It taught me how to talk about mathematics. In 1967 I could not even dream that one day (2006) I will be invited to the most math                          fun math conference in the world - Gathering for Gardner - where I met most of the people I knew from Gardner's books. Thank you for the inspiration, Martin Gardner!

Obituary in New York Times 
A Flexagon for Martin Gardner
For 35 years he was writing columns for Scientific American
Discover magazine blog with many other people telling how much Gardner has inspired them

And here is what Martin Gardner's friend of 50 years wrote:


Written by James Randi 
Saturday, 22 May 2010 18:14
Martin Gardner has died.  I have dreaded to type those words, and Martin would not have wanted to know that I'm so devastated at what I knew - day to day - had to happen very soon.  I'm glad to report that his passing was painless and quick.  That man was one of my giants, a very long-time friend of some 50 years or so.  He was a delight, a very bright spot in my firmament, one to whom I could always turn to with a question or an idea, with any strange notion I could invent, and with any complaint or comment I could come up with.

I never had an angry word with Martin. Never. It was all laughs and smiles, all the best of everything.

Forgive me for writing this without any editing.  It's just as it occurs to me.

I can't quite picture my world without him, and just yesterday I printed up a new set of mailing labels for him, plus stationery, which didn't get mailed. For the last few years I supplied him with that small favor, assuring him that he should notify me when he ran out, but he never did, because he thought it was too much trouble for me. Only when I received a letter from him last week that was hand-addressed, did I know that it was time for another shipment to Oklahoma.

He was such a good man, a productive and useful member of our society, and I can anticipate the international reaction to his passing.  His books - so many of them - remain to remind us of his contributions to us all.  His last one was dedicated to me, and I am just so proud of that fact, so very proud

It will take a while, but Martin would want me to get on with my life, so I will.

It's tough 


How can this be true?
This is Martin Gardner's modified version of Curry's paradox. An extensive history and explanations are given in [Martin Gardner, 1956]. See also [Frederickson, 1997]. The picture made Daniel Takacs.


  1. Viss lielais taisnstūris būtu 13x5= 65 rūtiņas. Tātad jebkuram no abiem lielo trijstūru laukumiem būtu jābūt 32.5 rūtiņas.
    Laukums pirmajam trijst = 5 (mazais trijst) + 12 (lielais trijst) + 7 (dzeltenā figūra) + 8 (zaļā figūra) = 32 rūtiņas.
    Laukums otrajam trijst = 5 (mazais trijst) + 12 (lielais trijst) + 7 (dzeltenā figūra) + 8 (zaļā figūra) + 1 (tukšums) = 33 rūtiņas.
    Izrādās trijstūri nav vienādi...
    Pirmajā bildē papildinot abus (zaļo un sarkano) trijstūrus līdz taisnstūrim, pāri paliktu 2x8 taisnstūris kā otrajā bildē. Tātad pirmā trijst laukums 32 + otrā trijst laukums 33 = taisnstūra laukums 65. Veselos skaitļos rēķinot viss ir pareizi. Ir kaut kāds āķis ar nepilnajām rūtiņām...

  2. ja, patiesam sis paradokss ir balstits uz veselo skaitlu nepilnibam un parada, ka vajadzigi "labaki" skaitli - realie skaitli.Ta ka Gardners ieguva filozogijas bakalaura gradu, tad vins ari so paradoksu atvasinaja no filozofijas - te par to paradoksu ir vairak:'s_paradox

  3. Hmmm... I've3 seen this puzzle before (In one of Martin Garnner's books, probably) and was totally baffled by it, but now I can see visually that the outer "triangle" isn't actually triangular. Its "hypotenuse" is slightly concave in the first drawing because of the different slopes of the blue and red triangles, and slightly convex in the second for the same reason. The extra square is the difference in area between the two. The puzzle works by pretending that the red, blue and outer triangles are all the same shape, which they aren't--i.e. that 13/8 = 8/3 = 5/2.

    And the reason that the slopes look the same, and that the two small triangles can be arranged inside the big one, is that the side lengths are taken from the Fibonacci sequence, meaning that their ratios are successive approximations to 2.618...

    The discrepancy could be made more visible to the eye by attempting to fit a 3x1 triangle and a 5x2 triangle inside an 8x3 one.

    I loved Martin Gardner's books--I think I was about 10 when I was introduced to them.