College Geometry A Unified Development

ISBN-10: 1439819114

ISBN-13: 9781439819111

Edition: 2011

Authors: David C. Kay

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Description:

This text presents a unified treatment of the three classical geometries: Euclidean, hyperbolic, and spherical (elliptic). This unique approach of combining all three geometries simultaneously using twelve concise axioms has never appeared in book form before at this level. The text introduces each axiom, including its reasons for use and implications, and then explains it in detail. In addition to numerous figures, examples, and exercises, the book includes Geometer's Sketchpad to help students build and investigate math models, objects, figures, and graphs. The author provides programs for students to use on a supporting website. A solutions manual is available for qualifying instructors.
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Book details

List price: $148.99
Copyright year: 2011
Publisher: CRC Press LLC
Publication date: 6/24/2011
Binding: Hardcover
Pages: 652
Size: 7.00" wide x 10.00" long x 1.25" tall
Weight: 2.838
Language: English

Preface
Author
Lines, Distance, Segments, and Rays
Intended Goals
Axioms of Alignment
A Glimpse at Finite Geometry
Metric Geometry
Eves' 25-Point Affine Geometry: A Model for Axioms 0-4
Distance and Alignment
Properties of Betweenness: Segments and Rays
Coordinates for Rays
Geometry and the Continuum
Segment Construction Theorems
Angles, Angle Measure, and Plane Separation
Angles and Angle Measure
Plane Separation
Consequences of Plane Separation: The Postulate of Pasch
The Interior of an Angle: The Angle Addition Postulate
Angle Construction Theorems
Consequences of a Finite Metric
Unified Geometry: Triangles and Congruence
Congruent Triangles: SAS Hypothesis
A Metric for City Centers
The SAS Postulate and the ASA and SSS Theorems
Euclid's Superposition Proof: An Alternative to Axiom 12
Locus, Perpendicular Bisectors, and Symmetry
The Exterior Angle Inequality
Inequalities for Triangles
Further Congruence Criteria
Special Segments Associated with Triangles
Quadrilaterals, Polygons, and Circles
Quadrilaterals
Congruence Theorems for Convex Quadrilaterals
The Quadrilaterals of Saccheri and Lambert
Polygons
Circles in Unified Geometry
Three Geometries
Parallelism in Unified Geometry and the Influence of �
Elliptic Geometry: Angle-Sum Theorem
Pole-Polar Theory for Elliptic Geometry
Angle Measure and Distance Related: Archimedes' Method
Hyperbolic Geometry: Angle-Sum Theorem
A Concept for Area: AAA Congruence
Parallelism in Hyperbolic Geometry
Asymptotic Triangles in Hyperbolic Geometry
Euclidean Geometry: Angle-Sum Theorem
Median of a Trapezoid in Euclidean Geometry
Similar Triangles in Euclidean Geometry
Pythagorean Theorem
Inequalities for Quadrilaterals: Unified Trigonometry
An Inequality Concept for Unified Geometry
Ratio Inequalities for Trapezoids
Ratio Inequalities for Right Triangles
Orthogonal Projection and �Similar� Triangles
Unified Trigonometry: The Functions c(�) and s(�)
Trigonometric identities
Classical Forms for c(�) and s(�)
Lambert Quadrilaterals and the Function C(u)
Identities for C(u)
Classical Forms for C(u)
The Pythagorean Relation for Unified Geometry
Classical Unified Trigonometry
Beyond Euclid: Modern Geometry
Directed Distance: Stewart's Theorem and the Cevian Formula
Formulas for Special Cevians
Circles: Power Theorems and Inscribed Angles
Using Circles in Geometry
Cross Ratio and Harmonic Conjugates
The Theorems of Ceva and Menelaus
Families of Mutually Orthogonal Circles
Transformations in Modern Geometry
Projective Transformations
Affine Transformations
Similitudes and Isometries
Line Reflections: Building Blocks for Isometries and Similitudes
Translations and Rotations
Circular Inversion
Non-Euclidean Geometry: Analytical Approach
Law of Sines and Cosines for Unified Geometry
Unifying Identities for Unified Trigonometry
Half-Angle Identities for Unified Geometry
The Shape of a Triangle in Unified Geometry: Cosine Inequality
The Equations of Gauss: Area of a Triangle
Directed Distance: Theorems of Menelaus and Ceva
Poincar�'s Model for Hyperbolic Geometry
Other Models: Surface Theory
Hyperbolic Parallelism and Bolyai's Ideal Points
Sketchpad Experiments
Intuitive Spherical Geometry
Proof in Geometry
The Real Numbers and Least Upper Bound
Floating Triangles/Quadrilaterals
Axiom Systems for Geometry
Solutions to Selected Problems
Bibliography
Index
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