Complex Numbers and Geometry
Complex Numbers and Geometry by Liang-shin Hahn, published by the American Mathematical Society on December 26, 2019, is a 192-page exploration of the interplay between complex numbers and geometry. This book aims to illustrate how these two mathematical concepts can be integrated, leading to straightforward proofs and natural extensions of various theorems in plane geometry, including the Napoleon theorem and the Ptolemy-Euler theorem. It is written in English and is designed to be accessible, requiring no prior knowledge of complex numbers.
Readers will find that the book is self-contained and can be approached at a comfortable pace, making it suitable for a one-semester course. Many chapters are designed to stand alone, allowing for flexible reading. The inclusion of over 100 exercises enhances the learning experience, making it appropriate for use as a text in geometry courses, problem-solving seminars, or as supplementary material for students seeking to deepen their understanding of the subject.
Official synopsis Publisher
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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