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Geometry from Euclid to Knots

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ISBN-10: 0486474593

ISBN-13: 9780486474595

Edition: 2010

Authors: Saul Stahl

List price: $31.00
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Description:

Tracing the formal development of Euclidean geometry, this text closely follows Euclid's classic,Elements.In addition to providing a historical perspective on plane geometry, it covers related topics, including non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, knots and links, and informal topology. Includes 1,000 practice problems. Solutions available. 2003 edition.
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Book details

List price: $31.00
Copyright year: 2010
Publisher: Dover Publications, Incorporated
Publication date: 3/18/2010
Binding: Paperback
Pages: 480
Size: 6.10" wide x 9.21" long x 0.98" tall
Weight: 1.562
Language: English

Preface to the Dover Edition
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