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Survey of Classical and Modern Geometries With Computer Activities

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ISBN-10: 0130143189

ISBN-13: 9780130143181

Edition: 2001

Authors: Arthur Baragar

List price: $117.80
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Description:

This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition. Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research. Ideal for geometry at an intermediate level.
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Book details

List price: $117.80
Copyright year: 2001
Publisher: Prentice Hall PTR
Publication date: 12/20/2000
Binding: Paperback
Pages: 384
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.452
Language: English

Introduction
The Geometry of Our World
A Review of Terminology
Notes on Notation
Notes on the Exercises
Euclidean Geometry
The Pythagorean Theorem
The Axioms of Euclidean Geometry
SSS, SAS, and ASA
Parallel Lines
Pons Asinorum
The Star Trek Lemma
Similar Triangles
Power of the Point
The Medians and Centroid
The Incircle, Excircles, and the Law of Cosines
The Circumcircle and the Law of Sines
The Euler Line
The Nine Point Circle
Pedal Triangles and the Simson Line
Menelaus and Ceva
Geometry in Greek Astronomy
The Relative Size of the Moon and Sun
The Diameter of the Earth
The Babylonians to Kepler, a Time Line
Constructions Using a Compass and Straightedge
The Rules
Some Examples
Basic Results
The Algebra of Constructible Lengths
The Regular Pentagon
Other Constructible Figures
Trisecting an Arbitrary Angle
Geometer's Sketchpad
The Rules of Constructions
Lemmas and Theorems
Archimedes' Trisection Algorithm
Verification of Theorems
Sophisticated Results
Parabola Paper
Higher Dimensional Objects
The Platonic Solids
The Duality of Platonic Solids
The Euler Characteristic
Semiregular Polyhedra
A Partial Categorization of Semiregular Polyhedra
Four-Dimensional Objects
Hyperbolic Geometry
Models
Results from Neutral Geometry
The Congruence of Similar Triangles
Parallel and Ultraparallel Lines
Singly Asymptotic Triangles
Doubly and Triply Asymptotic Triangles
The Area of Asymptotic Triangles
The Poincare Models of Hyperbolic Geometry
The Poincare Upper Half Plane Model
Vertical (Euclidean) Lines
Isometries
Inversion in the Circle
Inversion in Euclidean Geometry
Fractional Linear Transformations
The Cross Ratio
Translations
Rotations
Reflections
Lengths
The Axioms of Hyperbolic Geometry
The Area of Triangles
The Poincare Disc Model
Circles and Horocycles
Hyperbolic Trigonometry
The Angle of Parallelism
Curvature
Tilings and Lattices
Regular Tilings
Semiregular Tilings
Lattices and Fundamental Domains
Tilings in Hyperbolic Space
Tilings in Art
Foundations
Theories
The Real Line
The Plane
Line Segments and Lines
Separation Axioms
Circles
Isometries and Congruence
The Parallel Postulate
Similar Triangles
Spherical Geometry
The Area of Triangles
The Geometry of Right Triangles
The Geometry of Spherical Triangles
Menelaus' Theorem
Heron's Formula
Tilings of the Sphere
The Axioms
Elliptic Geometry
Projective Geometry
Moving a Line to Infinity
Pascal's Theorem
Projective Coordinates
Duality
Dual Conics and Brianchon's Theorem
Areal Coordinates
The Pseudosphere in Lorentz Space
The Sphere as a Foil
The Pseudosphere
Angles and the Lorentz Cross Product
A Different Perspective
The Beltrami-Klein Model
Menelaus' Theorem
Finite Geometry
Algebraic Affine Planes
Algebraic Projective Planes
Weak Incidence Geometry
Geometric Projective Planes
Addition
Multiplication
The Distributive Law
Commutativity, Coordinates, and Pappus' Theorem
Weak Projective Space and Desargues' Theorem
Nonconstructibility
The Field of Constructible Numbers
Fields as Vector Spaces
The Field of Definition for a Construction
The Regular 7-gon
The Regular 17-gon
Modern Research in Geometry
Pythagorean Triples
Bezout's Theorem
Elliptic Curves
A Mixture of Cevians
A Challenge for Fermat
The Euler Characteristic in Algebraic Geometry
Lattice Point Problems
Fractals and the Apollonian Packing Problem. S