99 Points of Intersection99个相交点
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作者： Hans Walser，Jean Pedersen著，Peter Hilton编
出 版 社：
出版时间： 2006-6-1字数：版次： 1页数： 153印刷时间： 2006/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780883855539包装： 精装内容简介
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.
作者简介
Hans Walser is lecturer at the Swiss Federal Instititute of Technology and the University of Basel.
目录
Author's Foreword
Foreword to the English Edition
Author's Note to the English Edition
1 What's it all about?
1.1 If three lines meet
1.1.1 The dodecagon
1.1.2 A puzzle
1.1.3 Points of intersection of circles
1.2 Flowers for Fourier
1.2.1 An example
1.2.2 Background
1.3 Chebyshev and the Spirits
1.3.1 Chebyshev Polynomials
1.3.2 Points of intersection in the Golden Sectior
1.3.3 An optical effect
1.4 Sheaves generate curves
1.4.1 Sheaves of straight lines
1.4.2 Sheaves of circles
2 The 99 points of intersection
3 The background
3.1 The four classical points of intersection
3.2 Proof strategies
3.2.1 The classical proof: the dialogue
3.2.2 Proofs by calculation
3.2.3 Dynamic Geometry Software
3.2.4 Affine invariance
3.3 Central projection
3.4 Ceva's Theorem
3.4.1 Giovanni Ceva
3.4.2 Examples
3.4.2.1 The center of gravity
3.4.2.2 The point of intersection of altitudes
3.4.3 The angle version of Ceva's Theorem
3.4.4 Generalization of the angle version
3.4.4.1 General n-gons
3.4.4.2 Spherical triangles
3.5 Jacobi's Theorem
3.5.1 A general theorem about points of intersection
3.5.2 Jacobi's Theorem as a special case
3.5.3 Kiepert's Hyperbola
3.6 Remarks on selected points of intersection
3.6.1 Point of intersection 32
3.6.1.l Points of intersection 36 to 40
3.6.2 Point of intersection 79
3.6.3 Point of intersection 84
3.6.3.1 Pythagoras' Theorem as a special case of the Law of Cosines
3.6.3.2 A "Pythagoras-free" derivation of the Law of Cosines
3.6.3.3 Points of intersection
3.6.4 Point of intersection 87
3.6.5 Points of intersection 96, 97, 98
References
Index
About the Author