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 proportion or ratio between two segments, not as a number), and Pythagorean triples, which go back to the Babylonians. These are closely related to the important rational parametrization of a circle, essentially discovered by Euclid and Diophantus. This is a valuable and under-appreciated insight which high school students ought to explicitly see. In fact young people learning mathematics should really see more of the history of the subject! The Greeks thought of mathematics differently than we do today, and all students can benefit from a closer appreciation of the difficulties which they saw, but which we today largely ignore. This series has now been extended a few times--with more than 35 videos on the History of Mathematics. ************ Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon: / njwildberger Your support would be much appreciated. Wild Egg Maths YT channel: https://www.youtube.com/channel/UCriF... Insights into Mathematics Playlists: • The Algebra of Boole, Logic and Circuit An... (31 videos) • Box Arithmetic: a new framework for Mathem... (18 videos) • Hypergroups and Diffusion Symmetry: an int... (6 videos) • Rational Trigonometry for maths, physics a... (4 videos) • Sociology and Pure Maths (44 videos) • Old Babylonian mathematics and Plimpton 322 (8 videos) • Math Foundations (226 videos) • Math Seminars N J Wildberger (26 videos) • Math History (ancient to modern) (45 videos) • Geometric Linear Algebra (43 videos) • Algebraic Topology (40 videos) • Universal Hyperbolic Geometry (55 videos) • Differential Geometry (34 videos) • Elementary Probability and Statistics (8 videos) • Math Terminology for Incoming Uni Students (9 videos) • Famous Math Problems ( 46 videos) • Elementary Mathematics Explained (K-6) (40 videos) • Ancient Mathematics and insights of Howard... (7 videos) • Wild West Banking: A mathematician goes We... (7 videos) • Playing Go: the ancient oriental board game (19 videos) • Maths and Music (21 videos) • Year 9 Mathematics (review fractions, deci... (10 videos) • Wild Trig: An introduction to Rational Tri... (94 videos) Wild Egg Maths Playlists: • Intro to Algebraic Calculus with Box Arith... (4 videos) • Classical to Quantum (for Members) (64 videos) • Solving Polynomial Equations and the Geode... (45 videos) • De Casteljau Bezier curves and associated ... (20 videos) • Exploring q-series (for Members) (8 videos) • Six: A mathematical exploration (9 videos) • Algebraic Calculus One: a new foundation f... (52 videos) • Advice to prospective research mathematici... (9 videos)
