Complex Numbers and Geometry (Mathematical Association of America Textbooks) [Paperback]

Liang-shin Hahn (Author)

Book Description

ISBN-10: 0883855100 | ISBN-13: 978-0883855102 | Publication Date: September 5, 1996 | Edition: 2

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.

Editorial Reviews

Review

'Provides a self-contained introduction to complex numbers and college geometry written in an informal style with an emphasis on the motivation behind the ideas ... The author engages the reader with a casual style, motivational questions, interesting problems and historical notes.' Mathematical Reviews

Book Description

This book demonstrates how complex numbers and geometry can be blended together beautifully, resulting in easy proofs and natural generalizations of many theorems in plane geometry. The book is suitable as a text for a geometry course, or for self-study. It 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.

Product Details

• Paperback: 204 pages
• Publisher: The Mathematical Association of America; 2 edition (September 5, 1996)
• Language: English
• ISBN-10: 0883855100
• ISBN-13: 978-0883855102
• Product Dimensions: 8.5 x 5.8 x 0.5 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #612,160 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

19 of 20 people found the following review helpful:

4.0 out of 5 stars New ways to do old things, March 27, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Complex Numbers and Geometry (Mathematical Association of America Textbooks) (Paperback)

Proofs in "pure" geometry are easy to understand but difficult to conceive. When presented with the opportunity to do such proofs, many people suffer from a brain cramp similar to that experienced by writers. One of the most common phrases heard when I was teaching is similar to the following, "I can follow the proof once it is done, but how do you think of trying those steps?" In this book, the author performs a marriage of complex numbers and geometry that can sometimes serve to point the aspiring geometer in the proper direction.
Contrary to their name, complex numbers are easy to understand and manipulate. Only basic knowledge of algebra is essential. In this case, the author uses all of Chapter One to introduce the fundamental ideas of their use. After that, things get exciting. Applying this knowledge to geometry, we see new ways to do old, sometimes very old things. In many cases, the approach is general, in that it is easy to see how such ideas can be used to attack other problems. Large numbers of exercises are included at the end of each chapter.
Worthy of inclusion in any library, this author shows that it is always possible to develop new ways to solve old problems.

Published in Journal of Recreational Mathematics, reprinted with permission.