Less Annoying Hyperbolic Surfaces
I already wrote about my first experience crocheting hyperbolic surfaces. In my first surface I added two more stitches per current stitch. It took me hours to crochet the last row: the same hours it took me to crochet the rest.
For my next project, I reduced the ratio. The light blue thingy has ratio 3/2. I continued making my life simpler. The next project, the purple surface on the left, has ratio 4/3. The last project on the right has a ratio of 5/4 and is my favorite. Mostly because I am lazy and it was the fastest to make.
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Math for the knitting masses – The nth Root:
[…] For my next project, I reduced the ratio. The light blue thingy has ratio 3/2. I continued making my life simpler. The next project, the purple surface on the left, has ratio 4/3. The last project on the right has a ratio of 5/4 and is my favorite. Mostly because I am lazy and it was the fastest to make. … (Tanya Khovanova’s Math Blog) […]
20 January 2019, 7:03 pmJim Stevenson:
This is a rather belated response to your post “The Annoyance of Hyperbolic Surfaces”. I had not paid too much attention to these types of knitting or crocheting efforts, but your reference to exponential growth and a surface of constant negative curvature prompted me to explore the idea more deeply. (My interest was further fueled, of course, by the delightful humor of your tale.) I developed one light-weight post on the exponential growth (https://josmfs.net/2019/02/22/exponential-yarn/), but then got tangled in a deeper post on the constant negative curvature (https://josmfs.net/2019/02/24/bugles-trumpets-and-beltrami/), where I got off the track through an over-simplification and misunderstanding. It is amazing what one can learn doing a detailed example. I thank you for the stimulus to tackle such a problem. I should also say I have enjoyed a number of your other posts. (I was led to your involvement with the Coffin Problems from Nakul Dawra’s GoldPlatedGoof Youtube site and his presentation of the background and some examples.)
24 February 2019, 2:26 pmJF Peltier:
Crocheting hyperbolic surfaces is very nice!
28 February 2019, 9:11 amWhile playing with neodymium magnet balls, I did all sorts of spheres by removing some shapes that paves the plane, and then instead of removing I started adding more “fabric” of space and got hyperbolic surfaces.
Like for crochet, the easiest way is to make concentric circles of length greater than 6n, for example 7n or 8n… this is the equivalent to adding stiches every rank.