Euclidean plane geometry | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-02

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Euclidean_geometry


00:01:56 1 The iElements/i
00:03:22 1.1 Axioms
00:05:34 1.2 Parallel postulate
00:06:49 2 Methods of proof
00:08:42 3 System of measurement and arithmetic
00:10:45 4 Notation and terminology
00:10:55 4.1 Naming of points and figures
00:11:25 4.2 Complementary and supplementary angles
00:12:12 4.3 Modern versions of Euclid's notation
00:13:01 5 Some important or well known results
00:13:12 5.1 Pons Asinorum
00:13:51 5.2 Congruence of triangles
00:14:27 5.3 Triangle angle sum
00:14:55 5.4 Pythagorean theorem
00:15:23 5.5 Thales' theorem
00:15:54 5.6 Scaling of area and volume
00:16:50 6 Applications
00:18:55 7 As a description of the structure of space
00:20:43 8 Later work
00:20:52 8.1 Archimedes and Apollonius
00:21:44 8.2 17th century: Descartes
00:23:13 8.3 18th century
00:23:42 8.4 19th century and non-Euclidean geometry
00:24:21 8.5 20th century and general relativity
00:26:05 9 Treatment of infinity
00:27:48 9.1 Infinite objects
00:29:28 9.2 Infinite processes
00:29:38 10 Logical basis
00:31:17 10.1 Classical logic
00:32:13 10.2 Modern standards of rigor
00:32:22 10.3 Axiomatic formulations
00:32:49 10.4 Constructive approaches and pedagogy
00:34:36 11 See also
00:36:44 11.1 Classical theorems
00:38:32 12 Notes
00:39:10 13 References



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SUMMARY
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Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only over short distances (relative to the strength of the  gravitational field).Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects, all without the use of coordinates to specify those objects. This is in contrast to analytic geometry, which uses coordinates to translate geometric propositions into algebraic formulas.