So over the summer, I got inspired by Vi Hart talking about hyperbolic planes in one of her videos (anyone surprised?) and decided to crochet one since it looked cool, and I had nothing better to do. (Once again, the fact that it’s taken me this long to blog about it shows how much busier I’ve been.)
Now, you’re probably wondering what the heck a hyperbolic plane actually is. I could give you the dictionary definition, “a two-dimensional vector space E on which there is a nondegenerate, symmetric or alternating form ƒ(x,y) such that there exists a nonzero element w in E for which ƒ(w,w) = 0.” I’ve also read somewhere that a hyperbolic plane is like the opposite of a sphere, since a sphere closes in on itself, and a hyperbolic plane just keeps expanding and growing. Oh right, there’s another definition that states that a hyperbolic plane has negative Gaussian curvature.
Yeah, I don’t really know what any of that means either. But I kind of understand the concept after making this, although I’m not sure how people visualized hyperbolic geometry without a model like this or even got the idea for it. Supposedly, it was invented to disprove the parallel postulate. I’m not anywhere near an expert on this subject, but apparently on a hyperbolic plane, there’s more than one line that goes through a point and is parallel to another line. Amazingly, crocheting is one of the few ways to actually model this.
After playing with this for a while, I tried somewhat organizing this……plane so it wouldn’t just be a big floppy thing, but my attempts at folding it in half ended up something like this:
|Trust me, I tried pretty hard, but it just wouldn’t cooperate.|
I thought that looked like a flower, so then I recrumpled it again, and took a few more pictures.
|Looking back on these three photos, it seems like my hand is getting taken over by hyperbolic-plane-ia|
|I was trying to flatten it to see what it would look like…..|