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Contenido

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.

   INDICE: Part I. What's 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. Ceva's Theorem; 5. Jacobi's Theorem; 6. Remarks on selected points of intersection; References.

Detalles del artículo

• Páginas : 153
• Editorial : MATHEMATICAL ASSOCIATION OF AMERICA
• Idioma : Inglés
• Fecha de Publicación : 01/04/2007
• ISBN: 9780883855539
• Encuadernación : Cartoné
• Nº Volúmenes : 1
• País de Publicación : Estados Unidos