Euclidean Geometry and Transformations

By: CLAYTON W. DODGE

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Paperback | 18 May 2004

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304 Pages

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23.5 x 15.5 x 1.91

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This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition. "A good textbook." - Mathematical Gazette. This introduction to Euclidean geometry emphasizes both the theory and the practical application of isometries and similarities to geometric transformations. Each chapter begins with an optional commentary on the history of geometry. Contents include modern elementary geometry, isometries and similarities in the plane, vectors and complex numbers in geometry, inversion, and isometries in space. Numerous exercises appear throughout the text, many of which have corresponding answers and hints at the back of the book. Prerequisites for this text, which is suitable for undergraduate courses, include high school algebra, geometry, and elementary trigonometry. 1972 edition.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Geometry

Modern Elementary Geometry
The Beginnings of Geometry	p. 1
Directed segments and angles	p. 4
Ideal points and ratios	p. 9
The theorem of Menelaus	p. 12
Ceva's theorem	p. 19
Some geometry of the triangle	p. 25
More geometry of the triangle	p. 33
Geometric constructions	p. 40
Isometries in the Plane
The Amazing Greeks	p. 48
Introduction to translations, rotations, and reflections	p. 50
Introduction to isometries	p. 55
Transformation theory	p. 59
Isometries as products of reflections	p. 63
Translations and rotations	p. 68
Halfturns	p. 72
Products of reflections	p. 74
Properties of isometries; a summary	p. 77
Applications of isometries to elementary geometry	p. 79
Further elementary applications	p. 83
Advanced applications	p. 87
Analytic representations of direct isometries	p. 93
Analytic representations of opposite isometries	p. 97
Similarities in the Plane
The rebirth of mathematical thinking	p. 101
Introduction to similarities	p. 104
Homothety	p. 106
Similarity	p. 110
Applications of similarities to elementary geometry	p. 114
Further elementary applications	p. 119
Advanced applications	p. 124
Analytic representations of similarities	p. 128
Vectors and Complex Numbers in Geometry
The search for the meaning of complex numbers	p. 131
Introduction to complex numbers	p. 134
Vectors	p. 138
Vector multiplication	p. 143
Vectors and complex numbers	p. 150
Triangles in the Gauss plane	p. 155
Lines in the Gauss plane	p. 161
The circle	p. 165
Isometries and similarities in the Gauss plane	p. 168
Inversion
Matchless modern mathematics	p. 171
Inversion	p. 175
Progressions, ratios, and Peaucellier's cell	p. 180
Inversion and complex geometry	p. 185
Applications of inversion	p. 189
Isometries in Space
What next?	p. 196
Introduction to three dimensions	p. 201
Reflection in a plane	p. 204
Basic space isometries	p. 208
More space isometries	p. 211
Some applications	p. 218
Analytic representations	p. 222
Appendixes
A Summary of Book I of Euclid's Elements	p. 226
Basic Ruler and Compass Constructions	p. 228
Bibliography	p. 232
Hints for Selected Exercises	p. 235
Answers	p. 248
Index	p. 288
Table of Contents provided by Ingram. All Rights Reserved.

Euclidean Geometry and Transformations

At a Glance

Paperback

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How to return your order

Defective items

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