Here_s an interesting thing. The juggli

Here's an interesting thing. The juggling prop called a diabolo has the s...
Tim HuttonTim Hutton - 2014-11-17 13:20:51+0000 - Updated: 2014-11-17 13:45:18+0000
Here's an interesting thing. The juggling prop called a diabolo has the same curvature as a torus. I discovered this while crocheting. I was making a torus and before sewing the edges together I realised that the surface would sit quite happily (no crumpling) in either pose. Like popping a rubber hemisphere in and out.

The torus/diabolo has negative curvature in the middle (the hyperboloid bit) and positive curvature elsewhere, with two circles of zero curvature in between. Presumably the popping only affects the region of positive curvature.

There's one other zero-energy configuration, not shown, where one side is popped out but not the other.

Has this sort of thing been studied? What other curved surfaces have multiple zero-energy configurations?
Shared with: Public, Paul Fisher
Paul Fisher - 2014-11-17 14:41:10+0000
If you make a saddle shape (a hyperbolic paraboloid) you can rotate the parts of it which go “up” versus “down” around the center. Even if you build it out of rigid sticks that are joined together, you can snap the up vs. down “corners” from one pair to the other.
Tim Hutton - 2014-11-17 15:04:04+0000 - Updated: 2014-11-17 15:53:42+0000
+Paul Fisher Interesting, thanks! I made this hyperboloid recently:
Hyperbola from Sticks | English | Straight Line to Curve 
but I think you're talking about something else. Are there instructions to make it somewhere?
Paul Fisher - 2014-11-17 16:57:16+0000
I’m referring to this shape:

For instance, if you could force the train station roof in the picture to flex, you could switch it so that the “up” and ”down” corners were in the opposite configuration, with all the straight lines still remaining straight (after the flexing process was complete, that is).
Tim Hutton - 2014-11-17 17:17:03+0000 - Updated: 2014-11-17 17:19:58+0000
OK, I'll try making one. I'll use the same skewer and loom bands construction method as in the video I mentioned, since that worked really well. I'm curious though, +Paul Fisher, what physical hyperbolic paraboloid have you flexed? Is there a common thing around, like a section of milk carton or something?

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