99 POINTS OF INTERSECTION

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Hans Walser is lecturer at the Swiss Federal Instititute of Technology and the University of Basel.A collection of surprising concurrences of lines with some typical methods for proving their existence.The 99 points of intersection presented here were collected during a yearlong 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.The 99 points of intersection presented here were collected during a yearlong 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.The 99 points of intersection presented here were collected during a yearlong 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.Part I. Whats It All About?: 1. If three lines meet: 2. Flowers for Fourier: 3. Chebyshev and the Spirits: 4. Sheaves generate curves: Part II. The 99 points of intersection: Part III. The Background: 1. The four classical points of intersection: 2. Proof strategies: 3. Central projection: 4. Cevas Theorem: 5. Jacobis Theorem: 6. Remarks on selected points of intersection: References.

Data Publikacji: 2006-09-14
Wymiary: 228 mm 152 mm 13 mm 357 gr