eBook Math Explained: The Britannica Guide to Geometry, 1st Edition

  • Published By:
  • ISBN-10: 1615302174
  • ISBN-13: 9781615302178
  • DDC: 516.009
  • Grade Level Range: 9th Grade - 12th Grade
  • 288 Pages | eBook
  • Original Copyright 2011 | Published/Released April 2012
  • This publication's content originally published in print form: 2011
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About

Overview

More than a study of shapes and angles, geometry reflects an amalgamation of discoveries over time. This book not only provides readers with a comprehensive understanding of geometric shapes, axioms, and formulas, it presents the field's brilliant minds—from Euclid to Wendelin Werner and many in between—whose works reflect a progression of mathematical thought throughout the centuries and have helped produce the various branches of geometry as they are known today. Detailed diagrams illustrate various concepts and help make geometry accessible to all.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Contents.
Introduction.
1: History of Geometry.
2: Ancient Geometry: Practical and Empirical.
3: Ancient Geometry: Abstract and Applied.
4: Ancient Geometry: Cosmological and Metaphysical.
5: The Post-Classical Period.
6: Transformation.
7: Relaxation and Rigour.
8: Branches of Geometry.
9: Euclidean Geometry.
10: Analytic Geometry.
11: Projective Geometry.
12: Differential Geometry.
13: Non-Euclidean Geometry.
14: Topology.
15: Graph Theory.
16: Biographies.
17: Ancient Greek and Islamic Geometers.
18: Pre-Modern (Pre-1800) Geometers.
19: Modern Geometers.
20: Appendix of Geometric Terms and Concepts.
21: Algebraic Surface.
22: Angle Trisection: Archimedes’ Method.
23: Angle Trisection: Quadratrix of Hippias.
24: Axiom.
25: Axiomatic Method.
26: Brachistochrone.
27: Bridge of Asses.
28: Brouwer’s Fixed Point Theorem.
29: Catenary.
30: Ceva’s Theorem.
31: Circle.
32: Compactness.
33: Cone.
34: Coordinate Systems.
35: Cross Ratio.
36: Curve.
37: Cycloid.
38: Cylinder.
39: Desargues’s Theorem.
40: Dimension.
41: Duality.
42: The Elements Since the Middle Ages.
43: Ellipse.
44: Ellipsoid.
45: Envelope.
46: Euclid’s Windmill.
47: Euclidean Space.
48: Method of Exhaustion.
49: Fractal.
50: Golden Ratio.
51: Graph.
52: Harmonic Construction.
53: Hausdorff Space.
54: Hilbert Space.
55: Hippocrates’ Quadrature of the Lune.
56: Hyperbola.
57: Hyperboloid.
58: Incommensurables.
59: Isometric Drawing.
60: Königsberg Bridge Problem.
61: Line.
62: Measuring the Earth, Classical and Arabic.
63: Measuring the Earth, Modern.
64: Metric Space.
65: Parabola.
66: Paraboloid.
67: Parallel Postulate.
68: Pencil.
69: Pi.
70: Platonic Solid.
71: Polygon.
72: Projection.
73: Pythagorean Theorem.
74: Space-Time.
75: Spiral.
76: Square.
77: Thales’ Rectangle.
78: Topological Space.
Glossary.
Bibliography.
Index.