Euclidean Geometry and Transformations by Dodge, Clayton W. -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Page Dedication Preface Contents Chapter 1 Modern Elementary Geometry

1 The Beginnings of Geometry Directed Segments and Angles 2 Directed Segments and Angles 3 Ideal Points and Ratios 4 The Theorem of Menelaus 5 Ceva’s Theorem 6 Some Geometry of the Triangle 7 More Geometry of the Triangle 8 Geometric Constructions

Chapter 2 Isometries in the Plane

9 The Amazing Greeks 10 Introduction to Translations, Rotations, and Reflections 11 Introduction to Isometries 12 Transformation Theory 13 Isometries as Products of Reflections 14 Translations and Rotations 15 Halfturns 16 Products of Reflections 17 Products of Isometrie; A Summary 18 Applications of Isometries to Elementary Geometry 19 Further Elementary Applications 20 Advanced Applications 21 Analytic Representations of Direct Isometries 22 Analytic Representations of Opposite Isometries

Chapter 3 Similarities in the Plane

23 The Rebirth of Mathematical Thinking 24 Introduction to Similarities 25 Homothety 26 Similarity 27 Applications of Similarities to Elementary Geometry 28 Further Elementary Applications 29 Advanced Applications 30 Analytic Representations of Similarities

Chapter 4 Vectors and Complex Numbers in Geometry

31 The Search for the Meaning of Complex Numbers 32 Introduction to Complex Numbers 33 Vectors 34 Vectors Multiplication 35 Vectors and Complex Numbers 36 Triangles in the Gauss Plane 37 Lines in the Gauss Plane 38 The Circle 39 Isometries and Similarities in the Gauss Plane

Chapter 5 Inversion

40 Matchless Modern Mathematics 41 Inversion 42 Progressions, Ratios, and Peaucellier’s Cell 43 Inversion and Complex Geometry 44 Applications of Inversion

Chapter 6 Isometries in Space

45 What Next? 46 Introduction to Three Dimensions 47 Reflection in a Plane 48 Basic Space Isometries 49 More Space Isometries 50 Some Applications 51 Analytic Representations

Appendixes

A. A Summary of Book I of Euclid’s Elements B. Basic Ruler and Compass Constructions

Bibliography Hints for Selected Exercises Answers Index