It was spring of 1977. I am a senior at the University of Latvia and counting the days to graduation in order to fulfill all those great dreams each of us have at that age. Still there are couple of classes to finish and one of them is Hyperbolic geometry. Although I was a good student in my other classes, I struggled with this one. By the end, I really disliked it.
The instructor drew two pictures on the chalkboard and claimed that in Euclidean geometry through the point outside the line you can draw only one line parallel to the given one but in Lobachevsky geometry (she used this name for hyperbolic geometry) those three intersecting lines are parallel to the one line below. „Why?” was this picture on the chalkboard showing what the instructor said it was supposed to show? She said, „You have to use your imagination or make an assumption.” How could I make an assumption if my previous experience told that only one of these lines would be parallel? , or how can I imagine something if I do not know what to imagine? Fortunately this was a pass/fail class. I passed – otherwise I would not be here – but I hoped I would never have to think about hyperbolic geometry again.
It was not in my dreams that 20 years later, I would be, on the other side of the world, faced with the task of teaching Fall semester hyperbolic geometry at Cornell University. There was no way I could use my previous „experie
We all learned in school that the sum of interior angles of a triangle is 180 degrees. That is true only on a Euclidean plane or zero curvature surface. On a sphere triangle will have angles which add up to more than 180 degrees. You can check this by cutting an apple.
On a hyperbolic plane, a triangle will have interior angles which add up to less than 180 degrees; and it means that we can have a triangle which has the sum of interior angles almost zero!
In first grade when I learned how to write numbers I had to do that neatly in a notebook with square graph paper.
This is a fragment of Latvian Project "From coral reefs to Baltic Sea" on exhibit here in Riga in 2009. Fortunately crocheting hyperbolic planes is not depriving people from their health and peace of mind but making them happy to become connected through the simple crochet pattern used in many creative ways – in physics, biology, in design, even psychotherapy, music, and poetry.
It was like a lightening from a clear sky when in March 2005 while gardening I received a phone call from Washington. Binnie Fry asked me if she could have some of my works for an art show Not the Knitting You Know in 1111 gallery on Pennsylvania Avenue. Yes, the same one that connects the United States Capitol to the White House. I authomatically said – yes, of course, but afterwards started to think – what should I do now? Before I used craft yarn for it was cheap and durable, and my models were made for use in geometry class not the art gallery. I did feel very scared but I had to keep my promise. First I went to the local yarn store to find some nice yarn, then I had to learn how to be an artist.
Since then I have been invited to participate in more than 20 art shows. One of my pieces even is included in Textile Collection of Cooper-Hewitt National Design Museum in New York City. I wish I could talk to my art teacher now. I wish no child would be told – you are no good at math. That is why I keep crocheting and talking about these hyperbolic planes.
Mathematics is not scary when you can touch it, think about it in fun ways, or even better – make it yourself. Charlotte Henderson after editing my book Crocheting Adventures with Hyperbolic Planes decided to crochet one herself. She said: „Once I had made one for myself, I was able to believe hyperbolic geometry properties that I had previously accepted with my head but not my heart.”