🚀 go-pugleaf

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."  There was a popular
article about them a few years ago; sorry, I don't recall the reference.
This topic was also covered in rec.puzzles last year, so there may be
some good stuff in the archive.

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.

An example of such a shape is three 60-degree circular arcs attached
end-to-end to form an "equilateral triangle" with bulging sides.
When you roll a block over this shape, as each "apex" of the shape
contacts the ground, it serves as the pivot for the arc bearing the
block, at whose center it happens to be.  A variant on this shape
is to draw a curve around it at a constant distance from the original
curve (e.g. roll a circle around the perimeter and trace the
envelope of its motion), resulting in a figure of six connected
circular arcs, three with smaller radius and three with larger radius.

I believe there are yet other shapes that have no circular arcs at
all, but can't recall one off-hand.

-- David Karr (karr@cs.cornell.edu)