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15 February 2004
Hypars
What: Hypars
By: various
From: See http://theory.lcs.mit.edu/~edemaine/hypar/ for a description of these things.
Why: Tom Hull came up to visit on a cold, bleary winter day, and so logically enough we spent the afternoon folding paper! One of the things we played with were these "Hypars" - forms approximating a hyperbolic paraboliod surface.
They're really cool. You can fold them out of any even-sided polygon. As you fold them they suddenly refuse to lie flat any longer, and start forming their characteristic shape. There's an amazing amount of tension in the paper from these seemingly innocuous nested "rings" of alternate mountain/valley creases. One of the odd things you can do with them once they're folded is flip pairs of neighboring points back and forth, which does some really odd things when you've made it from a shape with more than 4 corners.
I also decided to fold four, four-corner hypars from one piece of paper. (It seemed like a logical next thing to try.) It does work, but it's really hard to get the thing to collapse properly at the end, even though it sort of wants to go there... Hard to describe. Try it!
