Geometry for college students

Title:

Personal Author:

Isaacs, I. Martin, 1940-

Publication Information:

Pacific Grove, CA : Brooks/Cole Pub. Co., 2001

ISBN:

9780534351793

Subject Term:

Geometry

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000004377218	QA445 I63 2001	Open Access Book	Book	Searching... Unknown

1. THE BASICS Introduction and Apology / Congruent Triangles / Angles and Parallel Lines / Parallelograms / Area / Circles and Arcs / Polygons in Circles / Similarity 2. TRIANGLES The Circumcircle / The Centroid / The Euler Line, Orthocenter and Nine-Point Circle / Computations / The Incircle / Exscribed Circles / Morley's Theorem / Optimization in Triangles 3. CIRCLES AND LINES Simson Lines / The Butterfly Theorem / Cross Ratios / The Radical Axis 4. CEVA'S THEOREM AND ITS RELATIVE Ceva's Theorem / Interior and Exterior Cevians / Ceva's Theorem and Angles / Menelaus' Theorem 5. VECTOR METHODS OF PROOF Vectors / Vectors and Geometry / Dot Products / Checkerboards / A Bit of Trigonometry / Linear Operators 6. GEOMETRIC CONSTRUCTIONS Rules of the Game / Reconstructing Triangles / Tangents / Three Hard Problems / Constructible Numbers / Changing the Rules SOME FURTHER READING / INDEX

Chapter 1 The Basics	p. 1
1A Introduction and Apology	p. 1
1B Congruent Triangles	p. 5
1C Angles and Parallel Lines	p. 11
1D Parallelograms	p. 14
1E Area	p. 18
1F Circles and Arcs	p. 23
1G Polygons in Circles	p. 34
1H Similarity	p. 39
Chapter 2 Triangles	p. 50
2A The Circumcircle	p. 50
2B The Centroid	p. 56
2C The Euler Line, Orthocenter, and Nine-Point Circle	p. 60
2D Computations	p. 67
2E The Incircle	p. 73
2F Exscribed Circles	p. 80
2G Morley's Theorem	p. 82
2H Optimization in Triangles	p. 85
Chapter 3 Circles and Lines	p. 94
3A Simson Lines	p. 94
3B The Butterfly Theorem	p. 105
3C Cross Ratios	p. 107
3D The Radical Axis	p. 119
Chapter 4 Ceva's Theorem and Its Relatives	p. 125
4A Ceva's Theorem	p. 125
4B Interior and Exterior Cevians	p. 131
4C Ceva's Theorem and Angles	p. 136
4D Menelaus' Theorem	p. 146
Chapter 5 Vector Methods of Proof	p. 156
5A Vectors	p. 156
5B Vectors and Geometry	p. 158
5C Dot Products	p. 163
5D Checkerboards	p. 166
5E A Bit of Trigonometry	p. 170
5F Linear Operators	p. 172
Chapter 6 Geometric Constructions	p. 182
6A Rules of the Game	p. 182
6B Reconstructing Triangles	p. 187
6C Tangents	p. 191
6D Three Hard Problems	p. 196
6E Constructible Numbers	p. 203
6F Changing the Rules	p. 208
Some Further Reading	p. 216
Index	p. 218

Available:*

On Order

Summary

Summary

Table of Contents