Re: Balls (square wheels)

[Phil Parker <PPARKER@TWSUVM.UC.TWSU.EDU>]

> 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.