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source: njwildberger 2011年3月13日
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.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
MathHistory: A course in the History of Mathematics
Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, Stevin's decimal system, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology, the origins of group theory, hyperbolic geometry and more. Meant for a broad audience, not necessarily mathematics majors.
1a: Pythagoras' theorem 48:55
1b: Pythagoras' theorem (cont.) 23:26
2a: Greek geometry 50:41
2b: Greek geometry (cont.) 24:40
3a: Greek number theory 42:04
3b: Greek number theory (cont.) 24:41
4: Infinity in Greek mathematics 54:08
5a: Number theory and algebra in Asia 49:46
5b: Number theory and algebra in Asia (cont.) 22:53
6a: Polynomial equations 52:41
6b: Polynomial equations (cont.) 14:06
7a: Analytic geometry and the continuum 56:35
7b: Analytic geometry and the continuum 24:34
8: Projective geometry 1:09:42
9: Calculus 1:00:00
10: Infinite series 1:11:01
11: Mechanics and the solar system 51:03
12: Non-Euclidean geometry 50:52
13: The number theory revival 57:12
14: Mechanics and curves 57:51
15: Complex numbers and algebra 1:07:16
16: Differential Geometry 51:32
17: Topology 55:48
18: Hypercomplex numbers 59:31
19: Complex numbers and curves 57:56
20: Group theory 58:54
21: Galois theory I 43:54
21b: Galois theory II 29:56
22: Algebraic number theory and rings I 48:27
22b: Algebraic number theory and rings II 27:29
23: Simple groups, Lie groups, and the search for symmetry I 51:10
23b: Simple groups, Lie groups, and the search for symmetry II 26:26
24: Number systems and Stevin's decimals 52:20
25: Problems with the Calculus 48:48
26: Matrices, determinants and the birth of Linear Algebra 42:38
27: Sets, logic and computability 53:01
28: Computability and problems with Set theory 47:05
29: Combinatorics 41:01
30: Ancient astronomy in Babylon and China I 43:13
32: Astronomy and trigonometry in India 31:17
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