Softcover ISBN:  9781470466206 
Product Code:  PRB/27.S 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Electronic ISBN:  9781614444114 
Product Code:  PRB/27.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 

Book DetailsProblem BooksVolume: 27; 2016; 311 pp
This is a challenging problemsolving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the ninepoint circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral.
The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions.
This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class. 
Table of Contents

Chapters

Part I. Fundamentals

Chapter 1. Angle Chasing

Chapter 2. Circles

Chapter 3. Lengths and Ratios

Chapter 4. Assorted Configurations

Part II. Analytic Techniques

Chapter 5. Computational Geometry

Chapter 6. Complex Numbers

Chapter 7. Barycentric Coordinates

Part III. Farther from Kansas

Chapter 8. Inversion

Chapter 9. Projective Geometry

Chapter 10. Complete Quadrilaterals

Chapter 11. Personal Favorites

Part IV. Appendices

Appendix A. An Ounce of Linear Algebra

Appendix B. Hints

Appendix C. Selected Solutions

Appendix D. List of Contests and Abbreviations


Additional Material

Reviews

… A good understanding of high school geometry, and a fondness for solving problems, should be sufficient background for this book. … students preparing for mathematics competitions, and their faculty coaches, should find this book very valuable.
Mark Hunacek, MAA Reviews


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This is a challenging problemsolving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the ninepoint circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral.
The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions.
This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.

Chapters

Part I. Fundamentals

Chapter 1. Angle Chasing

Chapter 2. Circles

Chapter 3. Lengths and Ratios

Chapter 4. Assorted Configurations

Part II. Analytic Techniques

Chapter 5. Computational Geometry

Chapter 6. Complex Numbers

Chapter 7. Barycentric Coordinates

Part III. Farther from Kansas

Chapter 8. Inversion

Chapter 9. Projective Geometry

Chapter 10. Complete Quadrilaterals

Chapter 11. Personal Favorites

Part IV. Appendices

Appendix A. An Ounce of Linear Algebra

Appendix B. Hints

Appendix C. Selected Solutions

Appendix D. List of Contests and Abbreviations

… A good understanding of high school geometry, and a fondness for solving problems, should be sufficient background for this book. … students preparing for mathematics competitions, and their faculty coaches, should find this book very valuable.
Mark Hunacek, MAA Reviews