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Picture This

What 3 dimensional shape will pass through a rectangle, triangle and circle each time filling the whole space? The answer may surprise you in it's simplicity. Before I tell you what it is, see if you can visualize the shape using the following requirements.

Think about a circle and a cone. The cone is circular in its horizontal cross section, so it completely fills a circle when viewed along its axis from either the top or the bottom. Now think about the cone and the triangle: a cone is triangular in its vertical cross-section, and so fills a triangle shape when viewed orthogonally ' to its vertical axis'. Okay so far? Now think about what the problem requires. The object or shape must be circular in cross section one way, triangular in cross section from another direction and (here's the kicker...) square (or rectangular) in cross section from a third direction. Got it figured out yet?

Okay, I'll tell you how to get the answer. Start with a cylinder, like a round pencil or something similar. Then use a sharp knife to shave off one side at an angle. Turn the pencil (or whatever) through 180 degrees and shave off the other side so that you will have produced a wedge. Now cut the wedge part cleanly from the rest of the cylinder. The little piece that this produces should be circular when viewed from the bottom, triangular when viewed from one side, and square (or rectangular) when viewed from 90 degrees. I think what might throw you with this is that this shape doesn't have a regular name that we would be familiar with in everyday use. But it is the cylindrical wedge that you are looking for.


About the Author

Richard M. J. RenneboogRichard M. J. Renneboog, MS
Richard M. J. Renneboog is an independent private technical consultant and writer in both chemical and computer applications. Endeavors have included preparation of scripts for instructional and promotional video, corporate website design, curriculum development for training in advanced composites technology, and development.

Further Reading
Mathematical Origami: Geometrical Shapes by Paper Folding
by David Mitchell

Related Web Links

The Geometry Center
by Tamara Munzner

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