# 99 Points of Intersection

### By Hans Walser

Catalog Code: POI
Print ISBN: 978-0-88385-553-9
163 pp., Paperbound, 2001
List Price: $26.95 MAA Member:$21.95
Series: Spectrum

The 99 points of intersection presented here were collected during a year-long search for surprising concurrence of lines. For each example we find compelling evidence for the sometimes startling fact that in a geometric figure three straight lines, or sometimes circles, pass through one and the same point. Of course, we are familiar with some examples of this from basic elementary geometry—the intersection of medians, attitudes, angle bisectors, and perpendicular bisectors of sides of a triangle. Here there are many more examples—for figures other than triangles, some where even more than three straight lines pass through a common point.

The main part of the book presents 99 points of intersection purely visually. They are developed in a sequence of figures, many without caption or verbal commentary. In addition the book contains general thoughts on and examples of the points of intersection, as well as some typical methods for proving their existence. Many of the examples shown in the book were inspired by questions and suggestions made by students and high school teachers. Several of those examples have not only a geometrical but also an intriguing aesthetic aspect.

The book addresses high school students and students at the undergraduate level as well as their teachers, but will appeal to anyone interested in geometry.

### Table of Contents

Author’s Foreword
Foreword to the English Edition
Author’s Note to the English Edition
What’s it all about?
The 99 points of intersection
The background
References
Index
About the Author

### About the Author

Hans Walser was born in 1944 in Rheineck, Switzerland. He received his PhD in 1975 from the ETH Zurich (Swiss Federal Institute of Technology, Zurich). From 1975 to 2001 he was a teacher at the State College of Thurgau, Switzerland, and he was a visiting guest at Santa Clara University, California, in 1996 and 1998. Walser is now a lecturer at the ETH Zurich and the University of Basel. His primary research interest is geometry. He is a member of the Swiss Mathematical Society, the MAA, the AMS, and several German societies devoted to mathematics and teaching of mathematics. Walser is the author of numerous books. The MAA has already published translations of two other books: The Golden Section and Symmetry.

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