Home > Appreciation, Geometry > Twirling Tori

Twirling Tori

This is a mind-blowing animation of arms circulating around a torus, created by Emilio Gomariz.  I definitely became entranced for a bit, trying to follow a single hand all the way around the donut.  (Click the image or this link if you can’t see the animation).

Apart from being visually amaazing, this puts me in mind of a result about fluid flows on surfaces.  This animation demonstrates that a liquid, for example, can flow over the surface of a torus in such a way that every point moves:  nothing appears stationary here, and everything is moving in a smooth (i.e., continuous) fashion.

The remarkable result is that this same can not be done on the surface of a sphere!  There will always (at least) one point on the surface of the sphere that doesn’t move.  A popular interpretation of this result is that however windy it might be outside, there is always at least one point on the Earth that’s perfectly calm.

Seems like there are a lot of torii showing up in artwork lately.  Thanks to robotwisdom for linking to this.

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