Hyperbolic Crochet – Mini Coral Reef Installation

This project hit a lot of my happy points: fiber arts, math geekery, and nature worship.

So there’s a branch of mathematics called hyperbolic geometry.

I’m no mathematician, but I’ll try to summarize: if you took “regular” geometry in school, it was probably Euclidian geometry. For a long time, no one called it that because it was the only geometry, so it was just “geometry.”  Anything that happens on a plane in Euclidian geometry is assumed to happen on a flat 2 dimensional plane, like a piece of paper.

And you might remember one of the fundamental axioms of geometry, that if you have a straight line A and a point B that is not on that line:A line and a single point not on that line

then there is only one possible line that is both parallel to line A and runs through point B:
parallel lines

That’s pretty easy to understand when you hear it, because you can see it and touch it and draw it yourself.

So then back to hyperbolic (NON-Euclidian) geometry. It turns out that if your plane is NOT 2-D like a piece of paper, but curved in a way that makes the plane expand or contract as you go backward and forward (Huh? I know, stick with me…), then you *can* have two lines that cross each other at point B, but neither one will ever cross line A:

parallel lines on a hyperbolic plane

No way, right? It makes no sense, because I’m trying to show it on a 2D plane. For a long time, even super-brainy math majors were forced to just sort of bend the paper and “try and imagine it,” and wrap their brains around it the best they could. sometimes people tried to make models of it with paper in 3D, but it didn’t work very well.

Until one day a math professor, Daina Taimina, thought up the idea of building a model of a hyperbolic plane in crochet. It looked something like this:

crocheted hyperbolic plane

You start out with a simple straight line of say 20 crochet stitches, and then you add some stitches to the next row, and then add more stitches to each row until there are so many stitches in each row that it can’t lie flat and starts to fold over on itself. Voila! A touchable, foldable, hyperbolic plane.

And when you temporarily flatten out the plane to show where a “straight” line would go on this plane, and then “draw” a straight line on the plane using a string:





And then repeat the process with two more lines that cross each other:





You can now clearly see that on a hyperbolic plane the two crossing lines will never touch the third line even though all of them are straight lines!

Hyperbolic geometry is all wrapped up in a lot of complicated ideas like Einstein’s general theory of relativity and other things that are officially way over my head – but as usual, the internet will tell you all about it if you’re curious.

Nature is the best designer. It’s usually really hard for humans to make things that are anywhere near as beautiful as the flowing, irregular, organic shapes found in nature.

Well, it turns out that nature uses hyperbolic geometry to make a lot beautiful things:

Butter lettuce
Flickr image: Dwight Sipler
Flickr image: Liz West
Flickr image: Liz West
Lettuce slug
Flickr image: Laslo Ilyes – This one is an animal, not a plant – crazy!

Suddenly, thanks to Daina Taimina, people realized they could easily emulate the amazing forms found in shells and coral and seaweed in crochet. And crochet is easy, even for beginners.

People got very excited about this idea and started crocheting their own coral reefs:

Flickr image: Stitchlily
Flickr image: Stitchlily

The one pictured above is a small one – some of them fill entire rooms. Large-scale museum exhibits have been mounted, and they are incredible. A Google image search for “hyperbolic crochet” will provide you with more examples than I have room for here.

I was so inspired by the whole thing that I created my own miniature reef installation, shown in the first photo of this post.

And it really is SO easy to try. It takes about 5 minutes to learn the basic crochet stitch.

The supplies are cheap – grab yourself a basic crochet hook and some yarn, and you’re ready to go. If you decide to get more in depth, there are books you can get to show you how to do specific things, but really between YouTube and the many awesome web sites out there, you can (as usual) probably find what you need online.

Watching videos is not a substitute for making things, though – give it a try! And if you do, please send photos.

Go make something!