Crochet redux: The Anatomy of a Hyperbolic Plane Crocheted Around a Point

Note to my readers: This post was first published on May 18, 2010, under the title “The Anatomy of a Hyperbolic Plane Crocheted Around a Point.” I have also embedded a video at the end of the post of a talk given by, Daina Taimiņa, the mathematician who devised and then articulated directions for these wonderful objects. The video about 17 minutes long, and features some amazing hyperbolic planes, and well as the story of how the crocheted planes came to be.

Today would have been the perfect day to sit at home the entire day and do absolutely nothing but crochet and eat bon bons.

Instead the day was punctuated with just enough errands to make it difficult to make progress on any one project. Additionally, the project that is at the top of my to-be-finished list (the-afghan-that-has-eluded-me) is no longer anything remotely close to portable. I found myself wondering, “what’s a crocheter to do?”

In this instance, the crocheter in question (me) decided that a hyperbolic plane would be the perfect running-errands-on-a-rainy-day project. As a practical matter, however, I already have a collection of hyperbolic planes that could be described as small to medium in size and number. The question then became, what could I do that would add something that was missing to my current collection?

It turned out that the answer to the question was to crochet a series of seven hyperbolic planes that show how the effect of the increase round by round for seven rounds. Armed with a 4.5mm hook and a portable stash of Red Heart Super Saver yarn, I began the project as I waited for my son’s choir practice to end.

To show the increase as dramatically and quickly as possible, I started with 6 single crochet stitches in the first round and then set N=1. What this means in crochet terms, is that after I completed the sixth single crochet, I made two stitches in every stitch after that.

What follows is a series of photographs that demonstrates the progress and change over 7 rounds.

First round of a crochet hyperbolic plane
Round 1 = 6 single crochet

Second round of a crochet hyperbolic plane
Round 2 = 12 single crochet

Round 3 of a crochet hyperbolic plane
Round 3 = 24 single crochet

Round four of a crochet hyperbolic plane
Round 4 = 48 single crochet

Round 5 of a crochet hyperbolic plane
Round 5 = 96 single crochet

Round 6 of a crochet hyperbolic plane
Round 6 = 192 single crochet

Round 7 of a crochet hyperbolic plane
Round 7 = 384 single crochet

Seven crochet hyperbolic planes
Seven planes, all in a row

As you can see, there does not appear to be a whole lot going on in the first four rounds, but by the fifth round, the edge begins to show signs of some serious curing, and by the seventh round the edge is quite unruly.

So, if you have every struggled with making your own hyperbolic plane, or if you have not yet known the joys of making one, I hope you find the series of photos inspire to you to make one of your own.

Daina Taimiņa (the creator of hyperbolic crochet) in her own words: