Re: connected rings?

Aidan wrote:
Jay Linn wrote:
[...] These ideas tend
to fall by the wayside because the existing trimvirate of balls, ring,
clubs respectively exhibit three, two, and one axes of symmetry each, and
are therefore arguably pretty close to the ideal shapes for objects with
varying degrees of symmetry.

balls and rings both have an infinite number of axes of symmetry (arguably
clubs do too). Maybe you mean 3, 2 and 1 dimensions :)

Actually, I think Jay meant "principal axis of rotation." A ball has one,
and rings and clubs have two.
Any object with three (different) principal axes of rotation will have one
axis that is inherently unstable
--- and any object that isn't essentially a sphere, disc (ring), or
cylinder (club) will have three.

Try flipping a cigar box about each of the three axes perpendicular to its
faces. You'll see that it spins
nicely about the shortest and longest axes, but is wildly unstable about
the middle axis.

Why this is true is left as an exercise for the reader :-).

Greg



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