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by David Kay

Cover type: Print On DemandEdition: 2ND 01

Copyright: 2001

Publisher: Addison-Wesley Longman, Inc.

Published: 2001

International: No

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College Geometry is an approachable text, covering both Euclidean and Non-Euclidean geometry. This text is directed at the one semester course at the college level, for both pure mathematics majors and prospective teachers. A primary focus is on student participation, which is promoted in two ways: (1) Each section of the book contains one or two units, called Moments for Discovery, that use drawing, computational, or reasoning experiments to guide students to an often surprising conclusion related to section concepts; and (2) More than 650 problems were carefully designed to maintain student interest.

**Kay, David : University of North Carolina-Asheville **

(** Indicates optional section.*)

Preface.

To the Student.

**1. Exploring Geometry. **

Discovery in Geometry.

Variations on Two Familiar Geometric Themes.

*Ptolemy, Brahmagupta and the Quadrilateral.

A Glimpse at Modern Classical Geometry.

*Discovery via the Computer.

**2. Foundations of Geometry I: Points, Lines, Segments, and Angles. **

*An Introduction to Axiomatics and Proof.

*The Role of Examples and Models.

*An Excursion: Euclid's Concept of Area and Volume.

Incidence Axioms for Geometry.

Metric Betweeness, Segments, Rays, and Angles.

Plan Separation, Postulate of Pasch, Interiors of Angles.

Angle Measure and the Ruler, Protractor Postulates.

Crossbar Theorem, Linear Pair Axiom, Perpendicularity.

Chapter Summary.

**3. Foundations of Geometry II: Triangles, Quadrilaterals, and Circles. **

Triangles, Congruence Relations, SAS Hypothesis.

*Taxicab Geometry: Geometry Without SAS Congruence.

SAS, ASA, SSS Congruence, and Perpendicular Bisectors.

Exterior Angle Inequality.

The Inequality Theorems.

Additional Congruence Criteria.

Quadrilaterals.

Circles.

Chapter Summary.

**4. Euclidean Geometry: Trigonometry, Coordinates, and Vectors. **

Euclidean Parallelism, Existence of Rectangles.

Parallelograms and Trapezoids: Parallel Projection.

Similar Triangles, Pythagorean Theorem, Trigonometry.

*Regular Polygons, Tiling.

The Circle Theorems.

Coordinate Geometry and Vectors.

*Families of Orthogonal Circles, Circular Inversion.

*Some Modern Geometry of the Triangle.

Chapter Summary.

5. Transformations in Geometry.

Euclid's Superposition Proof and Plan Transformation.

Reflections: Building Blocks for Isometrics.

Translations, Rotations and Other Euclidean Motions.

Other Transformations.

Coordinate Characterization of Linear Transformations.

*Transformation Groups.

*Using Transformation Theory in Proofs.

Chapter Summary.

**6. Alternative Concepts for Parallelism: Non-Euclidean. **

*Historical Background of Non-Euclidean Geometry.

An Improbable Logical Case.

The Beltrami-Poincaré Half-Plan Model.

Hyperbolic Geometry 1: Angle Sum Theorem.

*Hyperbolic Geometry 2: Asymptotic Triangles.

*Hyperbolic Geometry 3: Theory of Parallels.

Models for Hyperbolic Geometry: Relative Consistency.

*Axioms for a Bounded Metric: Elliptic Geometry.

Chapter Summary.

**7. An Introduction to Three Dimensional Geometry. **

Orthogonality Concepts for Lines and Plans.

Parallelism in Space, Prisms, Pyramids, and Boxes.

Cones, Cylinders, and Spheres.

Volume in E^3.

Coordinates, Vectors, and Isometries in E^3.^

Spherical Geometry.

Appendixes.

A. Bibliography.

B. Solutions for Selected Problems.

C. Symbols, Axioms, Theorems.

Index.

- Windows 7/8, or Mac OS X 10.6 or above

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Summary
College Geometry is an approachable text, covering both Euclidean and Non-Euclidean geometry. This text is directed at the one semester course at the college level, for both pure mathematics majors and prospective teachers. A primary focus is on student participation, which is promoted in two ways: (1) Each section of the book contains one or two units, called Moments for Discovery, that use drawing, computational, or reasoning experiments to guide students to an often surprising conclusion related to section concepts; and (2) More than 650 problems were carefully designed to maintain student interest.

Author Bio

**Kay, David : University of North Carolina-Asheville **

Table of Contents

(** Indicates optional section.*)

Preface.

To the Student.

**1. Exploring Geometry. **

Variations on Two Familiar Geometric Themes.

*Ptolemy, Brahmagupta and the Quadrilateral.

A Glimpse at Modern Classical Geometry.

*Discovery via the Computer.

**2. Foundations of Geometry I: Points, Lines, Segments, and Angles. **

*The Role of Examples and Models.

*An Excursion: Euclid's Concept of Area and Volume.

Incidence Axioms for Geometry.

Metric Betweeness, Segments, Rays, and Angles.

Plan Separation, Postulate of Pasch, Interiors of Angles.

Angle Measure and the Ruler, Protractor Postulates.

Crossbar Theorem, Linear Pair Axiom, Perpendicularity.

Chapter Summary.

**3. Foundations of Geometry II: Triangles, Quadrilaterals, and Circles. **

*Taxicab Geometry: Geometry Without SAS Congruence.

SAS, ASA, SSS Congruence, and Perpendicular Bisectors.

Exterior Angle Inequality.

The Inequality Theorems.

Additional Congruence Criteria.

Quadrilaterals.

Circles.

Chapter Summary.

**4. Euclidean Geometry: Trigonometry, Coordinates, and Vectors. **

Parallelograms and Trapezoids: Parallel Projection.

Similar Triangles, Pythagorean Theorem, Trigonometry.

*Regular Polygons, Tiling.

The Circle Theorems.

Coordinate Geometry and Vectors.

*Families of Orthogonal Circles, Circular Inversion.

*Some Modern Geometry of the Triangle.

Chapter Summary.

5. Transformations in Geometry.

Euclid's Superposition Proof and Plan Transformation.

Reflections: Building Blocks for Isometrics.

Translations, Rotations and Other Euclidean Motions.

Other Transformations.

Coordinate Characterization of Linear Transformations.

*Transformation Groups.

*Using Transformation Theory in Proofs.

Chapter Summary.

**6. Alternative Concepts for Parallelism: Non-Euclidean. **

An Improbable Logical Case.

The Beltrami-Poincaré Half-Plan Model.

Hyperbolic Geometry 1: Angle Sum Theorem.

*Hyperbolic Geometry 2: Asymptotic Triangles.

*Hyperbolic Geometry 3: Theory of Parallels.

Models for Hyperbolic Geometry: Relative Consistency.

*Axioms for a Bounded Metric: Elliptic Geometry.

Chapter Summary.

**7. An Introduction to Three Dimensional Geometry. **

Parallelism in Space, Prisms, Pyramids, and Boxes.

Cones, Cylinders, and Spheres.

Volume in E^3.

Coordinates, Vectors, and Isometries in E^3.^

Spherical Geometry.

Appendixes.

A. Bibliography.

B. Solutions for Selected Problems.

C. Symbols, Axioms, Theorems.

Index.

Digital Rights
**eBook Requirements**
**VitalSource Bookshelf Reader**

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**Download Requirements:**
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**Digital Rights**

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Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

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**Copying:** Allowed, 2 selections may be copied every 180 days

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**Expires:** Yes, may be used for 180 days after activation

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**Sharing:** Not Allowed

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Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2001

International: No

Published: 2001

International: No

**Kay, David : University of North Carolina-Asheville **

(** Indicates optional section.*)

Preface.

To the Student.

**1. Exploring Geometry. **

Variations on Two Familiar Geometric Themes.

*Ptolemy, Brahmagupta and the Quadrilateral.

A Glimpse at Modern Classical Geometry.

*Discovery via the Computer.

**2. Foundations of Geometry I: Points, Lines, Segments, and Angles. **

*The Role of Examples and Models.

*An Excursion: Euclid's Concept of Area and Volume.

Incidence Axioms for Geometry.

Metric Betweeness, Segments, Rays, and Angles.

Plan Separation, Postulate of Pasch, Interiors of Angles.

Angle Measure and the Ruler, Protractor Postulates.

Crossbar Theorem, Linear Pair Axiom, Perpendicularity.

Chapter Summary.

**3. Foundations of Geometry II: Triangles, Quadrilaterals, and Circles. **

*Taxicab Geometry: Geometry Without SAS Congruence.

SAS, ASA, SSS Congruence, and Perpendicular Bisectors.

Exterior Angle Inequality.

The Inequality Theorems.

Additional Congruence Criteria.

Quadrilaterals.

Circles.

Chapter Summary.

**4. Euclidean Geometry: Trigonometry, Coordinates, and Vectors. **

Parallelograms and Trapezoids: Parallel Projection.

Similar Triangles, Pythagorean Theorem, Trigonometry.

*Regular Polygons, Tiling.

The Circle Theorems.

Coordinate Geometry and Vectors.

*Families of Orthogonal Circles, Circular Inversion.

*Some Modern Geometry of the Triangle.

Chapter Summary.

5. Transformations in Geometry.

Euclid's Superposition Proof and Plan Transformation.

Reflections: Building Blocks for Isometrics.

Translations, Rotations and Other Euclidean Motions.

Other Transformations.

Coordinate Characterization of Linear Transformations.

*Transformation Groups.

*Using Transformation Theory in Proofs.

Chapter Summary.

**6. Alternative Concepts for Parallelism: Non-Euclidean. **

An Improbable Logical Case.

The Beltrami-Poincaré Half-Plan Model.

Hyperbolic Geometry 1: Angle Sum Theorem.

*Hyperbolic Geometry 2: Asymptotic Triangles.

*Hyperbolic Geometry 3: Theory of Parallels.

Models for Hyperbolic Geometry: Relative Consistency.

*Axioms for a Bounded Metric: Elliptic Geometry.

Chapter Summary.

**7. An Introduction to Three Dimensional Geometry. **

Parallelism in Space, Prisms, Pyramids, and Boxes.

Cones, Cylinders, and Spheres.

Volume in E^3.

Coordinates, Vectors, and Isometries in E^3.^

Spherical Geometry.

Appendixes.

A. Bibliography.

B. Solutions for Selected Problems.

C. Symbols, Axioms, Theorems.

Index.

- Windows 7/8, or Mac OS X 10.6 or above

eTextbooks and eChapters can be viewed by using the free reader listed below.

Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.

Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.

Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

VitalSource Bookshelf

**Copying:** Allowed, 2 selections may be copied every 180 days

**Printing:** Allowed, 2 prints for 180 days

**Expires:** Yes, may be used for 180 days after activation

**Reading Aloud:** Allowed

**Sharing:** Not Allowed

**Min. Software Version:** VitalSource Bookshelf

**Suitable Devices:** PCs, Tablet PCs, Macs, Laptops

**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

**Digital Rights Management (DRM) Key**

**Printing** - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."

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**Min. Software Version** - This is the minimum software version needed to read this book.

**Suitable Devices** - Hardware known to be compatible with this book. Note: Reader software still needs to be installed.