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SQUARE WHEELS

1999 William Beaty

Imagine a solid cube. Inflate it a bit so it has a slight "pincusion" shape. Now drill a hole through it, through one pair of diagonal vertices. Stick two of these pincusioned-cubes on an axle. If the elliptical curves of the "pincusioned" edges are correct, then this device will roll perfectly smoothly, like a glass ball. Square wheels!

Or, recall that if you view a cube along its diagonal vertices, you see a hexagon. If you bend the edges of the cube outwards a little, then the hexagon becomes a circle. Circles can roll!

Or, imagine the volume which is created by the intersection of four cylinders passing through a central point. Now grind the pointed pyramids of this volume down, leaving only the "cube" edges. The result looks like a slightly-swollen cube. The edges are segments of ellipses. This cube can roll, if placed upon an axle.




In 1991 we had an RC car from Radio Shack with four polished plexiglass "square wheels" zooming around the lab. A pair of "square wheels" on an axle makes a great physics-paperweight. Triangular wheels look even stranger.

I wonder, was this my independent invention? Or is it already well known? I've never stumbled across any papers on "square wheels" since I started playing with them in 1991. I wouldn't be suprised if there was some obscure article about them in a journal somewhere.

Similar things can be done with a tetrahedron (triangular wheels), or most any polyhedron.

I came up with this while trying to think of some cool "science toy" to top Piet Hein's "Superegg". Square wheels is actually just a ripoff of the Exploratorium exhibit where thin inflated triangles are used as roller bearings (the edges of the triangle are segments of a circle, with center of curvature placed at the vertex opposite each side). Not a big leap from an inflated triangle to a rolling cube, eh? :)

 





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