Geometry from Euclid to Knots

Description

Cover; Title Page; Copyright Page; Dedication; Contents; Preface to the Dover Edition; Preface; 1 Other Geometries: A Computational Introduction; 1.1 Spherical Geometry; 1.2 Hyperbolic Geometry; 1.3 Other Geometries; 2 The Neutral Geometry of the Triangle; 2.1 Introduction; 2.2 Preliminaries; 2.3 Propositions 1 through 28; 2.4 Postulate 5 Revisited; 3 Nonneutral Euclidean Geometry; 3.1 Parallelism; 3.2 Area; 3.3 The Theorem of Pythagoras; 3.4 Consequences of the Theorem of Pythagoras; 3.5 Proportion and Similarity; 4 Circles and Regular Polygons; 4.1 The Neutral Geometry of the Circle.;Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, Elements. The text augments Euclid's statements with appropriate historical commentary and many exercises - more than 1,000 practice exercises provide readers with hands-on experience in solving geometrical problems. In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.