Tuesday, April 24, 2007

Essay—Cubes and Tablecloths

I remained cheerful during faculty meetings by practicing writing backwards, upside down, and upside down and backwards, with both hands and the high hope of reaching perfection. I also doodled a checkered cube repeatedly to a point of wretched excess. I enjoyed filling in every other little square, though I was never able to alternate the colors of the checkers with complete success.

Is it possible to checker a cube completely? I think checkers of the same color will invariably meet at four of the cube's twelve edges. (Fig. 1 shows one of these flawed edges.) I've discovered, however, two ways to steer clear of this problem:

You can insert a gusset (fig. 2). This enables the colors to alternate and, as a surprising consequence, suggests a tablecloth providing the opportunity for domestic elaborations. The transformation from cube to cloth is explored in "Tea Time" and "Tea'd Cube".

Or, if you're drawing a picture, you can simply eliminate the checkering problem by lopping off the offending checkers (fig. 3). This surgical method is used in "Blue Checkered Cloth" and "Spot of Sky".

As a way of circumventing a 3-D pattern problem, my
checkered tablecloth stands for an intuitive and comic leap of the imagination. In the final frame of "How to Checker a Cube", I'm looking through the window into my own imagination.
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