99 Points of Intersection: Examples-Pictures-Proofs

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MAA, Sep 14, 2006 - Mathematics - 153 pages
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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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The 99 points of intersection
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About the author (2006)

Hans Walser is lecturer at the Swiss Federal Instititute of Technology and the University of Basel.

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