Complex Numbers and Geometry (Mathematical Association of America Textbooks)

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully, resulting in easy proofs and natural generalizations of many theorems in plane geometry such as the theorems of Napoleon, Simson, Cantor and Morley.Beginning with a construction of complex numbers, readers are taken on a guided tour that includes something for everyone, even veteran professional mathematicians. Yet, the entire book is accessible to students at the high school level.The book is self-contained- no background in complex numbers is assumed- and it can be covered at a leisurely place in a one-semester course. Over 100 exercises are included. The book would be suitable as a text for a geometry course, for a problem solving seminar, or as enrichment for students who are interested in mathematics as part of culture. The Purpose Of This Book Is To Demonstrate That Complex Numbers And Geometry Can Be Blended Together Beautifully. This Results In Easy Proofs And Natural Generalizations Of Many Theorems In Plane Geometry, Such As The Napoleon Theorem, The Ptolemy-euler Theorem, The Simson Theorem, And The Morley Theorem. The Book Is Self-contained - No Background In Complex Numbers Is Assumed - And Can Be Covered At A Leisurely Pace In A One-semester Course. Many Of The Chapters Can Be Read Independently. Over 100 Exercises Are Included. The Book Would Be Suitable As A Text For A Geometry Course, Or For A Problem Solving Seminar, Or As Enrichment For The Student Who Wants To Know More. -- Provided By Publisher. 1. Complex Numbers -- 2. Applications To Geometry -- 3. Mobius Transformations -- Epilogue -- A. Preliminaries In Geometry -- B. New Year Puzzles. Liang-shin Hahn. Includes Bibliographical References (p. 165) And Index.