The four pillars of geometry
By: John Stillwell
Series: Undergraduate texts in mathematics; Undergraduate texts in mathematics
Publisher: Springer
Published: 2010
Place of publication: New York
Language: eng
Number of pages: 227
ISBN-13: 9781441920638
Subjects: Geometry; Textbooks
Notes: Includes bibliographical references (p. 213-214) and index.
Table of contents: title: Preface -- -- 1.; title: Straightedge and compass -- -- 1.1.; title: Euclid's construction axioms -- -- 1.2.; title: Euclid's construction of the equilateral triangle -- -- 1.3.; title: Some basic constructions -- -- 1.4.; title: Multiplication and division-- -- 1.5.; title: Similar triangles -- -- 1.6.; title: Discussion -- -- 2.; title: Euclid's approach to geometry -- -- 2.1. The; title: parallel axiom -- -- 2.2.; title: Congruence axioms -- -- 2.3.; title: Area and equality -- -- 2.4.; title: Area of parallelograms and triangles -- -- 2.5. The; title: Pythagorean theorem -- -- 2.6.; title: Proof of the Thales theorem -- -- 2.7.; title: Angles in a circle -- -- 2.8. The; title: Pythagorean theorem revisited -- -- 2.9.; title: Discussion -- -- 3.; title: Coordinates -- -- 3.1. The; title: number line and the number plane -- -- 3.2.; title: Lines and their equations -- -- 3.3.; title: Distance -- -- 3.4.; title: Intersections of lines and circles -- -- 3.5.; title: Angle and slope -- -- 3.6.; title: Isometries -- -- 3.7. The; title: three reflections theorem -- -- 3.8.; title: Discussion -- -- 4.; title: Vectors and euclidean spaces -- -- 4.1.; title: Vectors -- -- 4.2.; title: Direction and linear independence -- -- 4.3.; title: Midpoints and centroids -- -- 4.4. The; title: inner product -- -- 4.5.; title: Inner product and cosine -- -- 4.6. The; title: triangle inequality -- -- 4.7.; title: Rotations, matrices, and complex numbers -- -- 4.8.; title: Discussion --; title: 5.; title: Perspective -- -- 6.1.; title: Perspective drawing -- -- 5.2.; title: Drawing with straightedge alone -- -- 5.3.; title: Projective plane axioms and their models -- -- 5.4.; title: Homogeneous coordinates -- -- 5.5.; title: Projection -- -- 5.6.; title: Linear fractional functions -- -- 5.7. The; title: cross-ratio -- -- 5.8.; title: What is special about the cross-ratio? -- -- 5.9.; title: Discussion -- -- 6.; title: Projective planes -- -- 6.1.; title: Pappus and Desargues revisited -- -- 6.2.; title: Coincidences -- -- 6.3.; title: Variations on the Desargues theorem -- -- 6.4.; title: Projective arithmetic -- -- 6.5. The; title: field axioms -- -- 6.6. The; title: associative laws -- -- 6.7. The; title: distributive law -- -- 6.8.; title: Discussion -- -- 7.; title: Transformations -- -- 7.1. The; title: group of isometries of the plane -- -- 7.2.; title: Vector transformations -- -- 7.3.; title: Transformations of the projective line -- -- 7.4.; title: Spherical geometry -- -- 7.5. The; title: rotation group of the sphere -- -- 7.6.; title: Representing space rotations by quaternions -- -- 7.7. A; title: finite group of space rotations -- -- 7.8. The; title: groups S³ and RP³ -- -- 7.9.; title: Discussion -- -- 8.; title: Non-Euclidean geometry -- -- 8.1.; title: Extending the projective line to a plane -- -- 8.2.; title: Complex conjugation -- -- 8.3.; title: Reflections and Möbius transformations -- -- 8.4.; title: Preserving non-Euclidean lines -- -- 8.5.; title: Preserving angle -- -- 8.6.; title: Non-Euclidean distance -- -- 8.7.; title: Non-Euclidean translations and rotations -- -- 8.8.; title: Three reflections or two involutions -- -- 8.9.; title: Discussion --; title: References --; title: Index.