Geometry From Euclid to Knots

Name: Geometry From Euclid to Knots
Price: 9.18 USD
Availability: InStock
ISBN: 9780130329271

ISBN-10: 0130329274

ISBN-13: 9780130329271

Edition: 2003

Authors: Saul Stahl

List price: $114.67

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Description:

For Junior-level courses in Geometry. Designed to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text augments Euclid's elegant but sparse statements with appropriate historical commentary and many exercises. It also introduces the non-Euclidean geometries, allowing students to gain perspective and enhance their appreciation of axiomatic systems.

Book details

List price: $114.67
Copyright year: 2003
Publisher: Prentice Hall PTR
Publication date: 7/31/2002
Binding: Hardcover
Pages: 458
Size: 7.25" wide x 9.75" long x 0.75" tall
Weight: 1.892
Language: English



Preface



Other Geometries: A Computational Introduction



Spherical Geometry



Hyperbolic Geometry



Other Geometries



The Neutral Geometry of the Triangle



Introduction



Preliminaries



Propositions 1 through 28



Postulate 5 Revisited



Nonneutral Euclidean Geometry



Parallelism



Area



The Theorem of Pythagoras



Consequences of the Theorem of Pythagoras



Proportion and Similarity



Circles and Regular Polygons



The Neutral Geometry of the Circle



The Nonneutral Euclidean Geometry of the Circle



Regular Polygons



Circle Circumference and Area



Impossible Constructions



Toward Projective Geometry



Division of Line Segments



Collinearity and Concurrence



The Projective Plane



Planar Symmetries



Translations, Rotations, and Fixed Points



Reflections



Glide Reflections



The Main Theorems



Symmetries of Polygons



Frieze Patterns



Wallpaper Designs



Inversions



Inversions as Transformations



Inversions to the Rescue



Inversions as Hyperbolic Motions



Symmetry in Space



Regular and Semiregular Polyhedra



Rotational Symmetries of Regular Polyhedra



Monstrous Moonshine



Informal Topology



Graphs



Nodes and Arcs



Traversability



Colorings



Planarity



Graph Homeomorphisms



Surfaces



Polygonal Presentations



Closed Surfaces



Operations on Surfaces



Bordered Surfaces



Knots and Links



Equivalence of Knots and Links



Labelings



The Jones Polynomial



A Brief Introduction to The Geometer's Sketchpad



Summary of Propositions



George D. Birkhoff's Axiomatization of Euclidean Geometry



The University of Chicago School Mathematics Project's Geometrical Axioms



David Hilbert's Axiomatization of Euclidean Geometry



Permutations



Modular Arithmetic


Solutions and Hints to Selected Problems


Bibliography


Index