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Complex Numbers & Geometry

Complex Numbers & Geometry

By Liang-shin Hahn

Print ISBN: 978-0-88385-510-2
200 pp., Paperbound, 1994
List Price: $30.00
MAA Member: $22.50
Series: MAA Textbooks

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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 Napolean, Ptolemy-Euler, Simson, and Morley.

Beginning with a construction of complex numbers, readers are taken on a 140-page guided tour that includes something for everyone, even those with advanced degrees in mathematics. Yet, the entire book is accessible to a talented high-school student.

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.

Table of Contents

1. Complex Numbers
2. Applications to Geometry
3. Möbius Transformations
Preliminaries in Geometry
New Year Puzzles

About the Author

Liang-shin Hahn was born in Tainan, Taiwan. He received his Ph.D. from Stanford University, taught for a short time at Johns Hopkins University, and then moved to the University of New Mexico where he has been ever since. He has held visiting professor positions at the University of Seattle, the National Taiwan University (Taipei), the University of Tokyo, the International Christian University (Tokyo), and Sophia University (Tokyo), giving him the distinction of teaching mathematics in three countries and in three languages.


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