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Re: Balls (square wheels)



Date: Wed, 24 Feb 1999 06:24:42 -0800
From: William Beaty <billb@ESKIMO.COM>

In 1990 we had a Radio Shack RC car with four polished plexiglass "square
wheels" running around the lab. A pair of "square wheels" on an axle
makes a great physics-paperweight. Triangular wheels look even stranger.

I wonder, was this my independant invention? Or is it already well known?
I've never stumbled across any papers on "square wheels" since I started
playing with them in 1994. I wouldn't be suprised if there was some
obscure article about them in a journal somewhere.

I don't have any ready references at hand, but the standard phrase to
search the mathematical literature is "curves of constant width." This
would cover the profile curves of solid wheels, but I do not know the
standard phrase for them specifically. There is at least one film/video
on these curves (I believe from the MAA) which I've seen at math meetings.

Similar things can be done with a tetrahedron (triangular wheels), or
most any polyhedron.

Square wheels is actually just a ripoff of the
Exploratorium exhibit where swollen triangles are used as roller bearings
(the edges of the triangle are segments of a circle, with center of
curvature placed at the vertex opposite each side).

This is the standard construction and generalizes to odd-gons. It's also
the shape of the rotors in a Wankel engine, such as used by Mazda in some
of its offerings. Using spherical caps instead of circular arcs seems
the reasonable extrapolation to solids, but again, I don't *know*.

---------------------------------------------
Phil Parker pparker@twsuvm.uc.twsu.edu
Random quote for this second:
Do not drink coffee in early A.M.
It will keep you awake until noon.