Moment 4: a2 + b2 = c2
Probably no collection of the top ten moments in mathematical history would be complete without mention of the Pythagorean Theorem, as beat into the ground as it is. “a2 + b2 = c2” has been rattled off by more of my students than any other mathematical formula, even by students who have no idea what it’s called, for what it’s used or who are even in Geometry at the time.
However, just as we named America after Amerigo Vespucci because he first realized America was not the West Indies but in fact a new land mass, we may have mistakenly credited Pythagoras of Samos (born 2579 years ago) for the discovery of the now called “Pythagorean Theorem”. America was here and populated long before Vespucci arrived, and although it was probably Pythagoras or one of this students who proved the theorem [2, page 44], a2 + b2 = c2 may have a similar history.
Babylonian clay tablets created 3500 years ago, or 1000 years before Pythagoras’s time, show an awareness of the triangle’s special property. In 1922, George Arthur Plimpton bought and donated to Columbia University a tablet traced to modern day Iraq (ancient Babylonia) and dated to 3800 years ago. Plimpton recognized “Pythagorean triples” on the ancient clay tablet [2, page 34]. These triples, such as 3-4-5 or 5-12-13, represent right triangles whose a2 + b2 equal a square number. References to the theorem later named the “Pythagorean Theorem" also pop up in ancient Indian and Chinese cultures as well [4, page 26].
Pythagoras went on to found a school, and consequently a following and then a brotherhood, which fostered the learning of philosophy, mathematics and natural science. Adopted from the Hindus, the Pythagoreans’ philosophy was a belief that whole numbers ruled the universe. This idea was taught at Pythagoras’s school and in his brotherhood for centuries after he passed away [4, page 27].
The Pythagorean School may be long gone, but the Pythagorean Theorem still lives strong. There are many different ways to prove this theorem, but possibly the most fun is the one using water or this one with sand. (The outtakes at the end are worth watching!)
The Pythagorean Theorem was included in Euclid’s Elements, as one of the very last two propositions [4, page 73] in his extensive works.
Works Cited:
[2] Pickover, Clifford A., The Math Book, Sterling Publishing, New York, 2009
[4] Eves, Howard, Great Moments in Mathematics Before 1650, The Mathematical Association of America, 1983
[7] Weisstein, Eric W., "Pythagorean Theorem.", MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PythagoreanTheorem.html
[13] mathworld.wolfram.com/images/eps-if/PythagoreanTheoremShear_700.gif
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