99 Points of Intersection

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.

• Translated from the original German
• Readily accessible to students at the undergraduate level but will appeal to anyone interested in geometry
• The examples given have both geometrical interest and an intriguing aesthetic aspect