99 Points of Intersection: Examples-Pictures-Proofs
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5.0
A book by Hans Walser
This book is highly recommended for geometers of all ages and a wide range of expertise. It would be an excellent resource for a course taught with Dynamic Geomeetry Software. --Mary Coupland, Australian Mathematics Teacher
The interesting theme of this book is that it is often the case that when some lines intersect, there are others that must also be part of the same intersection. Furthermore, there must be a reason why they intersect. Walser uses diagrams to display the intersections and there are three sections in the book. The first section is the introduction, where equations and their corresponding figures are presented. Section two is a series of 99 diagrams where the emphasis is on how they intersect. Each starts with three small figures, which build towards the larger, complete structure. The third and final section is a brief description of some well-known geometric proofs such as Jacobi's Theorem, Kiepert's Hyperbola and Ceva's Theorem. I was fascinated with some of the 99 figures in the second section. They are designed to be understood as-is without having to resort to equations and textual descriptions. I found that to be the case, it was a rare instance when I had to look at the diagram for more than a few seconds before I understood it. This is an interesting way to teach the joy and wonder of mathematics. For in many cases if I had not seen the diagram, I would not have believed that so many different lines would have intersected the way they did. Especially when the intersection is a single point.
Published in Journal of Recreational Mathematics, reprinted with permission
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