Bibliograph

Geometry, plane and fancy, David A. Singer

Type

Label

Geometry, plane and fancy, David A. Singer

Language

eng

Bibliography note

Includes bibliographical references and index

Illustrations

illustrations

Index

index present

Literary Form

non fiction

Main title

Geometry

Nature of contents

bibliography

Oclc number

39031893

Responsibility statement

David A. Singer

Series statement

Undergraduate texts in mathematics

Sub title

plane and fancy

Summary

Geometry: Plane and Fancy offers a fascinating tour through parts of geometry that students are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well-known parallel postulate of Euclid. The author shows how alternatives to Euclid's fifth postulate lead to interesting and different patterns and symmetries. In the process of examining geometric objects, the author incorporates some graph theory, some topology, and the algebra of complex (and hypercomplex) numbers. Nevertheless, the book has only mild prerequisites. Readers are assumed to have had a course in Euclidean geometry (including some analytic geometry and some algebra) at the high school level. Although many concepts introduced are advanced, the mathematical techniques are not

Table Of Contents

Ch. 1. Euclid and Non-Euclid. 1.1. The Postulates: What They Are and Why. 1.2. The Parallel Postulate and Its Descendants. 1.3. Proving the Parallel Postulate -- Ch. 2. Tiling the Plane with Regular Polygons. 2.1. Isometries and Transformation Groups. 2.2. Regular and Semiregular Tessellations. 2.3. Tessellations That Aren't, and Some Fractals. 2.4. Complex Numbers and the Euclidean Plane -- Ch. 3. Geometry of the Hyperbolic Plane. 3.1. The Poincare disc and Isometries of the Hyperbolic Plane. 3.2. Tessellations of the Hyperbolic Plane. 3.3. Complex numbers, Mobius Transformations, and Geometry -- Ch. 4. Geometry of the Sphere. 4.1. Spherical Geometry as Non-Euclidean Geometry. 4.2. Graphs and Euler's Theorem. 4.3. Tiling the Sphere: Regular and Semiregular Polyhedra. 4.4. Lines and Points: The Projective Plane and Its Cousin -- Ch. 5. More Geometry of the Sphere. 5.1. Convex Polyhedra are Rigid: Cauchy's Theorem. 5.2. Hamilton, Quaternions, and Rotating the Sphere. 5.3. Curvature of Polyhedra and the Gauss-Bonnet Theorem -- Ch. 6. Geometry of Space. 6.1. A Hint of Riemannian Geometry. 6.2. What is Curvature? 6.3. From Euclid to Einstein

Classification

Creator