🚀 go-pugleaf

In article <1993Jan5.193711.7525@cs.cornell.edu> karr@cs.cornell.edu (David Karr) writes:
>In article <106199@bu.edu> tvaughan@buphyk.bu.edu (Timothy Vaughan) writes:
>>They are round so that they cannot fall through the manhole,
>>regardless of the orientation.
>
>Gee whiz, that's why!  I always thought it was because they are too heavy
>to carry, so you want to be able to roll them.  :-) :-)
>
>>Other shapes, anyone?
>
>There are plenty of shapes that meet the "don't fall through" criterion.
>They are called "curves of constant diameter."...
> ...
>An example of such a shape is three 60-degree circular arcs attached
>end-to-end to form an "equilateral triangle" with bulging sides....

True, but add another requirement that the cover can be fit in
regardless of its (planar) orientation, that is, there is no need to
rotate it to place it in a fitting position.
THEN we are left with only the circle.

# And I think this is practically important.

>Another application of curves of constant diameter is that logs with
>such a cross-section can be used as rollers, for example to move a
>large block of stone.

The problem is that they can't be used as "wheels" (not rollers),
because you can't put an axis that maintains constant height while
rotating (they make good toys, though).
Even as rollers, there may be problems; because:
* they have a particular orientation of stability (with the pointed edge
  up, lowest center of mass) so that the motion may be jerky (though
  this won't be a problem if we use multiple rollers with different
  orientations), and
* the pointed edge may damage the supported object (as well as the road
  surface).

-Yuzuru Hiraga