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Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads

£49.99

Part of MAA Problem Book Series

  • Author: Evan Chen, Massachusetts Institute of Technology
  • Date Published: December 2016
  • availability: Available in limited markets only
  • format: Paperback
  • isbn: 9780883858394

£ 49.99
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Description
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About the Authors
  • This challenging problem-solving book on Euclidean geometry requires nothing of the reader other than courage. Readers will encounter cyclic quadrilaterals, power of a point, homothety, and triangle centers, as well as such classical gems as the nine-point circle, the Simson line, and the symmedian. Both a traditional and a computational view of the use of complex numbers and barycentric coordinates is offered, while more advanced topics are covered in the final part. These include inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. 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 how one would invent the solution to begin with. Providing over 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.

    • Includes over 300 practice problems, of varying difficulty, taken from contests around the world
    • Worked examples explain not only the solutions to problems, but also how to invent solutions to begin with
    • Requires no prerequisites
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    Product details

    • Date Published: December 2016
    • format: Paperback
    • isbn: 9780883858394
    • length: 326 pages
    • dimensions: 254 x 177 x 17 mm
    • weight: 0.58kg
    • availability: Available in limited markets only
  • Table of Contents

    Preface
    Preliminaries
    Part I. Fundamentals:
    1. Angle chasing
    2. Circles
    3. Lengths and rules
    4. Assorted configurations
    Part II. Analytic Techniques:
    5. Computational geometry
    6. Complex numbers
    7. Barycentric coordinates
    Part III. Farther from Kansas:
    8. Inversion
    9. Projective geometry
    10. Complete quadrilaterals
    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
    Bibliography
    Index
    About the author.

  • Author

    Evan Chen, Massachusetts Institute of Technology
    Evan Chen is currently an undergraduate studying at the Massachusetts Institute of Technology. He won the 2014 USA Mathematical Olympiad, earned a gold medal at the IMO 2014 for Taiwan, and acts as a Problem Czar for the Harvard-MIT Mathematics Tournament.

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