--- In sliderule@y..., "Allen B, Carlisle" <profali5205@h...> wrote:

> I have a math problem that may confound and/or delight you menza

> folks out there. Draw an object that if slid through a one inch

> square hole in a sheet of metal so that there would be a point

> where no sunlight would seep through. This same abject could do

> the same thing going through a circle of one inch diameter and

> an equalateral triangle that measures an inch on each side.

> Good!.....Now what is the volume of this object???

Are you sure that the triangular hole is equilateral? I don't

think you can do that. Isoceles triangle, yes.

This is a pretty old problem, except for the equilateral part.

It can be found in _Puzzles Old & New_ by Hoffmann, originally

published in 1893. Reprinted by Sterling Publishers in 1997.

To construct the shape, start with a cylindrical cork 1 inch dia.

Cut it to 1 inch length. You now have a shape that will fit the

square and circular holes. Draw a line across the diameter of the

circle at one end. Make a sloping cut from that line down to the

circle at the other end, on each side. You now have a shape that

will fit a triangular hole.

Unfortunately, the triangular profile is one inch high and one inch

wide, so two sides of the triangle are sqrt(5/4), and it isn't

equilateral. Tonight my calculus doesn't feel up to finding

the volume, maybe it will feel better tomorrow.

carl