I am a math geek. I should point that out now.
I, therefore, think it’s so amazingly neat that someone figured out how to represent a hyperbolic surface using crochet! (That someone, by the way, was mathematician Daina Taimina.)
What is a hyperbolic surface, you may rightly ask. Well, it is defined as anything that expands exponentially away from a point in whatever direction you travel away from it. It also looks sort of like a loofa:
So, naturally, anything that is worked in spiral rows (like crochet) where the size of the next row is some multiple larger than the previous row can be said to be growing exponentially. And anything ‘hyperbolic’ can just as easily be represented by exponentials. Ergo, to make a hyperbolic crochet, like the one in the picture, the trick is to increase by the same amount, no matter what row you are on. For example, to make a ‘looser’ ripple of hyperbolic, you should increase every 3rd or 4th stitch. To make a super tight hyperbolic ripple, you should increase every stitch.
Even cooler than this: a bunch of people got together to recreate a coral reef using the method of hyperbolic crochet and display it at a museum! They have a blog with pictures and even some free patterns on how to do it here.
Now, you may be thinking, this sounds really fun and easy, I could make one of those little balls in no time! Let me warn you: the number of stitches that go into these things can be deceiving. Let’s say you start with 1 stitch and you want to double the number of stitches every row. You manage to squeeze 2 stitches into that one stitch, then, after that you would have rows with 4, then 8, then 16 stitches. So far so good? A mere two rows later you are dealing with 64 stitches. That will take a little time. Two rows after that? 256 stitches. You might have to put it down and come back to it after supper. At row 11, you will have to make 1024 stitches.
When they say ‘exponential’ they weren’t kidding, huh? Conclusion: I wouldn’t attempt one in a single sitting, but I would still attempt one. 😉