An edition of The four pillars of geometry
(2008)
The four pillars of geometry
by John C. Stillwell
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Book Details
Published in
New York
Table of Contents
Preface -- -- 1.
Straightedge and compass -- -- 1.1.
Euclid's construction axioms -- -- 1.2.
Euclid's construction of the equilateral triangle -- -- 1.3.
Some basic constructions -- -- 1.4.
Multiplication and division-- -- 1.5.
Similar triangles -- -- 1.6.
Discussion -- -- 2.
Euclid's approach to geometry -- -- 2.1. The
parallel axiom -- -- 2.2.
Congruence axioms -- -- 2.3.
Area and equality -- -- 2.4.
Area of parallelograms and triangles -- -- 2.5. The
Pythagorean theorem -- -- 2.6.
Proof of the Thales theorem -- -- 2.7.
Angles in a circle -- -- 2.8. The
Pythagorean theorem revisited -- -- 2.9.
Discussion -- -- 3.
Coordinates -- -- 3.1. The
number line and the number plane -- -- 3.2.
Lines and their equations -- -- 3.3.
Distance -- -- 3.4.
Intersections of lines and circles -- -- 3.5.
Angle and slope -- -- 3.6.
Isometries -- -- 3.7. The
three reflections theorem -- -- 3.8.
Discussion -- -- 4.
Vectors and euclidean spaces -- -- 4.1.
Vectors -- -- 4.2.
Direction and linear independence -- -- 4.3.
Midpoints and centroids -- -- 4.4. The
inner product -- -- 4.5.
Inner product and cosine -- -- 4.6. The
triangle inequality -- -- 4.7.
Rotations, matrices, and complex numbers -- -- 4.8.
Discussion --
5.
Perspective -- -- 6.1.
Perspective drawing -- -- 5.2.
Drawing with straightedge alone -- -- 5.3.
Projective plane axioms and their models -- -- 5.4.
Homogeneous coordinates -- -- 5.5.
Projection -- -- 5.6.
Linear fractional functions -- -- 5.7. The
cross-ratio -- -- 5.8.
What is special about the cross-ratio? -- -- 5.9.
Discussion -- -- 6.
Projective planes -- -- 6.1.
Pappus and Desargues revisited -- -- 6.2.
Coincidences -- -- 6.3.
Variations on the Desargues theorem -- -- 6.4.
Projective arithmetic -- -- 6.5. The
field axioms -- -- 6.6. The
associative laws -- -- 6.7. The
distributive law -- -- 6.8.
Discussion -- -- 7.
Transformations -- -- 7.1. The
group of isometries of the plane -- -- 7.2.
Vector transformations -- -- 7.3.
Transformations of the projective line -- -- 7.4.
Spherical geometry -- -- 7.5. The
rotation group of the sphere -- -- 7.6.
Representing space rotations by quaternions -- -- 7.7. A
finite group of space rotations -- -- 7.8. The
groups S³ and RP³ -- -- 7.9.
Discussion -- -- 8.
Non-Euclidean geometry -- -- 8.1.
Extending the projective line to a plane -- -- 8.2.
Complex conjugation -- -- 8.3.
Reflections and Möbius transformations -- -- 8.4.
Preserving non-Euclidean lines -- -- 8.5.
Preserving angle -- -- 8.6.
Non-Euclidean distance -- -- 8.7.
Non-Euclidean translations and rotations -- -- 8.8.
Three reflections or two involutions -- -- 8.9.
Discussion --
References --
Index.
Edition Notes
Includes bibliographical references (p. 213-214) and index.
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History
- Created June 30, 2019
- 3 revisions
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| December 13, 2022 | Edited by MARC Bot | import existing book |
| December 25, 2021 | Edited by ImportBot | import existing book |
| June 30, 2019 | Created by MARC Bot | Imported from Internet Archive item record. |