99 Points of Intersection: Examples-Pictures-Proofs by Hans Walser (PDF)

Description

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, altitudes, angle bisectors, and perpendicular bisectors of sides of a triangle. Here there are many more examples – some 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, developed in a sequence of figures. In addition the book contains general thoughts on and examples of the points of intersection, as well as some typical methods of proving their existence.

User’s Reviews

Editorial Reviews: Review 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 Book Description A collection of surprising concurrences of lines with some typical methods for proving their existence. Book Description 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. About the Author Hans Walser is lecturer at the Swiss Federal Instititute of Technology and the University of Basel. Read more

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