Pythagoras’ theorem (a) | Math History | NJ Wildberger

Pythagoras' theorem is both the oldest and the most important non-trivial theorem in mathematics. This is the first part of the first lecture of a course on the History of Mathematics, by N J Wildberger, the discoverer of Rational Trigonometry. We will follow John Stillwell's text Mathematics and its History (Springer, 3rd ed). Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. A few historical tidbits will be thrown in too... In this first lecture (with two parts) we first give a very rough outline of world history from a mathematical point of view, position the work of the ancient Greeks as following from Egyptian and Babylonian influences, and introduce the most important theorem in all of mathematics: Pythagoras' theorem. Two interesting related issues are the irrationality of the 'square root of two' (the Greeks saw this as a segment, or perhaps more precisely as the prop