99 Points of Intersection: Examples-Pictures-Proofs
- ISBN-10
- 0883855534
- ISBN-13
- 9780883855539
- Category
- Mathematics
- Pages
- 160
- Language
- English
- Published
- 2006-09-14
- Publisher
- MAA
- Author
- Hans Walser
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.
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