Math History/1

Pythagoras's Theorem A
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This is MATH 3560. The textbook is the first half of Mathematics and Its History by John Stillwell. There will be twelve lecture.

Pythagoras
600 BC is about when he lived. The history of ideas is his context. The Babylonians, Egyptian, Indians, and Chinese preceded him. The "Greek Period" was 700 BC to 300 AD. More famous than Pythagoras in this period were Euclid and Archimedes. This time was followed by the Arabs, then the Europeans (Newton, Euler, Gauss). The Greek Period was a region, not a people. Some were in Alexandria, Egypt. Archimedes was in Sicily.)

Theorem
3-4-5 is the oldest known triple. 9+16=25. In Modern parlance, $$d_1^2 + d_2^2 = d_3^2$$. However, the Greeks thought area was fundamental, so they wouldn't have written it this way. Euclid's Elements, Proposition 47/48, states it in terms of area. It was not about lengths.

Square roots were not typically done, and not needed, because they dealt in terms of areas. In modern vocabulary, there were no irrational numbers, just Natural Numbers. We really get it backwards, defining distance by using Pythagoras's theorem.

Thales
Thales was very likely Pythagoras's teacher. Pythagoras went on to start a school of thought, of which we know a great deal more than we do of Pythagoras himself. Their motto was that everything could be understood in terms of numbers. Their first, best example, was that consonant harmonies and melodic intervals were ratios of whole numbers. Doctor Wilderberg then proves that root-2 is not rational. According to legend, the man who leaked this proof was drowned.

Pythagoras's Theorem B
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