## Hyperbolic Plane – Knit or Crochet?

May.30, 2009

Now maths is a mystery to me.

When I discovered the crocheted Hyperbolic Plane and looked at a sites where crochet has been used to create the hyperbolic plane, I found this paper Crocheting the Hyperbolic Plane updated version is published in Mathematical Intelligencer, Vol. 23, No. 2, pp. 17-28, Spring 2001 .

It is said one cannot use knitting to create a Hyperbolic Plane as it is not rigid enough. Well that works for me because I don’t want to create a Hyperbolic Plane I just want to play with my yarn.

To create a knitted or crocheted Hyperbolic Plane you must create your piece with your stitch increases one row to the next occuring in a constant ratio and that ratio determines the radius of the hyperbolic plane.

I thought that is fine – but I don’t want to create the mathematical tool the Hyperbolic Plane – but what would happen if I knitted a scarf starting with a circle on a circular needle and increasing the stitches at a constant rate on every row. Generally when one increases in knitting or crochet the increases occur at a given interval to create a specific shape – a triangle, a bell, and so on. But the increases are not every 20 stitches or whatever increase range you decide on -they are usually on every second row and the increases form a part of the pattern.

I used a 4 ply (sock weight yarn) varigated yarn and created my stitch increases with Yarn Overs and of course because the increases are constant the Yarn Overs do not create a pattern. I placed markers every 50 stitches and moved them along on every row as I knitted to keep track of the numbers. Unfortunately when I was heading for the cast off row – which related to the number of stitches that I could manage on my circular needle, I was also knitting and talking to my husband and so I did not count the stitches as I cast off but I think I was well over 2000 in the number of stitches. I can probably work it out from the number of rows etc – but I don’t much like that math stuff – so I will have to do it again and with a longer circular needle – and then record properly the numbers and besides that will be more fun – creating another one – and this knitting is all about having fun.

The result looks like a fungus growing on the bark of a very old cherry tree in our garden in New Zealand, or it could look like some very sensitve soft seaweed which moves underwater with the movement of the waves.

I don’t mind and you can judge for yourself.