By David Eugene Smith

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D. Bernal and G. D. Scott. They compressed ball bearings in various packings and determined that the FCC, the face centered cubic packing of chapter 1, produced the tightest packing. Hales’s somewhat faulty conclusion did confirm Kepler’s observation, however. After seeds and peas have been squashed and squeezed, they will all be touched by twelve neighbors. If seeds accidentally found themselves placed along parallel rows and columns, and seeds of the next higher planes came to lie exactly above the ones of the lower planes, they would become cubes when pressed together.

But this was not the Woodstock generation, and rock music did not automatically mean pacifism. So at age nineteen Giuseppe Lodovico was appointed professor of mathematics at the Royal Artillery School of Turin. After all, not only artists needed a solid grounding in mathematics, as Dürer had pointed out; shooters too had to be able to compute where their shells would fall. While teaching artillery officers to do their math, Lagrange continued his research, and at the age of twenty-five he was already recognized as the foremost mathematician of his time.

Even the revolutionaries realized that some order was needed in the chaos that reigned in the markets. Merchants in different parts of the country used different modes of measurement (albeit keeping the price constant, which is a sure recipe for inflation), and the committee’s brief was to devise a system that would be binding throughout the country. After many hours of deliberation they came to the conclusion that the simple folk would find it easier to count and multiply if they could use their fingers.