## Bachet de Méziriac, Claude-Gaspar (1581–1638)Arithmetica, the book that Pierre de Fermat
was reading when he inscribed the margin with his famous Last
Theorem. Bachet is also remembered as a collector of mathematical puzzles, many of which, including river-crossing problems, measuring and weighing puzzles, number tricks, and magic squares, he published in Problèmes plaisans et délectables qui font
par les nombres (1612). One of the puzzles is to find the least number
of weights that can be used on a scale pan to weigh any integral number
of pounds from 1 to 40 inclusive, if the weights can be placed in either
of the scale pans. The answer is four: 1, 3, 9, and 27 pounds. On a slightly more serious note, Bachet observed that apparently every positive number can be expressed as a sum of at most four squares; for example, 5 = 2 ^{2} + 1^{2} , 6 = 2^{2} + 1^{2} + 1^{2},
7 = 2^{2} + 1^{2} + 1^{2} + 1^{2}, 8 = 2^{2}
+ 2^{2}, and 9 = 3^{2}. The case of 7 shows that sometimes
three squares wouldn't be enough. Bachet said he had checked this for more
than 300 numbers but didn't know how to prove it. It wasn't until the late
18th century that Joseph Lagrange supplied
a complete proof. ## Reference- Underwood, Dudley. "The First Recreational Mathematics Book."
*Journal of Recreational Mathematics*, 3, 164-169, 1970.
## Related category• MATHEMATICIANS | ||||||

Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Alternative Energy • Contact |