99 points of intersection : examples - pictures - proofs

著者

• Walser, Hans

書誌事項

99 points of intersection : examples - pictures - proofs

by Hans Walser ; translated from the original German by Peter Hilton and Jean Pedersen

（MAA spectrum）

Mathematical Association of America, 2006

タイトル別名

99 Schnittpunkte

Ninety-nine points of intersection

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

• 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA78234422
• ISBN:
  • 0883855534
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Washington, DC
• ページ数/冊数: xiv, 153 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA17084268