New ways to do old things

books:

	• Complex Numbers and Geometry (Mathematical Association of America Textbooks) Liang-shin Hahn The Mathematical Association of America, 1996 - 203 pages average customer review:based on 1 review view larger image
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New ways to do old things

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.

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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.

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