I took a nice break from my frustrations with value...I went to a workshop on hyperbolic planes given by Margaret Wertheim from the Institute for Figuring. It was given at a nice knitting shop; That Yarn Store, in Eagle Rock - never been to Eagle Rock - but it turned out to be a fairly cute little town on the way to Pasadena. Apparently the town was named after a rock which has a shadow of an eagle on it when the sun shines on it in a certain way.
It's pretty easy to understand parallel lines on a flat surface. It's gets a bit more complex to understand parallel lines on a sphere - reminded me of my celestial navigation days. But it's near impossible to imagine parallel lines on a hyperbolic plane - unless you know how to crochet. It is quite fascinating that it took a Latvian women who could crochet to finally in 1997 provide mathematicians with a way to actually touch and feel hyperbolic planes. Here is a photo of the some of the crocheted hyperbolic planes that Margaret had made. There are more on the website for the Institute of Figuring. There are some here and here and more here!
I took this picture to go with my notes that I took to document how to make each one of these different pieces. Fortunately, Margaret had also brought some copies of her book, A Field Guild to Hyperbolic Space; An Exploration of the Intersection of Higher Geometry and Feminine Handicraft. A nice compact book with the mathematical history and background of hyperbolic planes plus pictures and instructions on how to make the many kinds. I bought one. I couldn't resist. The book has the instructions and black and white photos. Colored ones are on the website.
I really liked what is called a pseudosphere which is made by crocheting in a spiral pattern then increasing by one stitch every three until you run out of yarn or get bored. Here is a picture of a pink pseudosphere. A pseudosphere is a hyperbolic plane which is wrapped around a cone point. I am currently crocheting one with my hand dyed self patterning yarn which is green with some yellow patches. I will post a photo when I am done...I have about five more rows to go - each row is doubling in size so it takes longer and longer to make one pass around. It's great to do while watching TV - - much easier than knitting - - and much more fun. [I obviously have not yet turned into a knitting knut...] I think I may try dyeing some yarn that would generate a better pattern and a unique look for this type of structure.
The Institute is putting together a display of a Coral Reef made of these crocheted hyperbolic planes. Perhaps, if one of mine comes out good, I'll send them one for their Coral Reef.