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1) The totally unprejudiced mind is playful and uninhibited, devising tasks for itself that seem to have no practical ends. For example, Piet Hein one day found himself pondering the columns of Copenhagen’s Town Hall.

He realized that by expanding...


2) ...each cylinder it would touch its neighbor along its full length and if the cylinders were rotated they would continue to touch.
3) He realized that they did not have to be cylindrical to continue to touch and rotate.
4) These two (at left) can touch in many variations but only two by two. Cylinders (center) can touch three by three. Are there non-cylindrical shapes that can do this?

5) There are: Piet Hein arrived at these twisted solids (called Corotoides) which are mathematically designed to touch two by two along their full length and three by three at one point every third of a turn. Any num ber of these rotating shapes can be com bined; four of them will transmit a uniform flow of energy. Technician friends inform Piet Hein that this freak of spatial geometry (described here for the first time) can be used for new kinds of conveyors, motors, pumps, crushing machines, compressors, etc. But Piet Hein invented the new shapes for shape’s sake. Now that he knows of their practical applications, however, he has patented them. Which is a solution of sorts, and which raises a problem.