Topics in elementary geometry

著者

• Bottema, O.

書誌事項

Topics in elementary geometry

O. Bottema

Springer, c2008

2nd ed

• : [pbk.]

タイトル別名

Hoofdstukken uit de elementaire meetkunde

注記

Includes bibliographical reference (p. [133]-137) and index

"With a Foreword by Robin Hartshorne"

"Translated from the Dutch by Reinie Erné"

"This current edition is a translation of the Second Dutch Edition of, Hoofdstukken uit de Elementaire Meetkunde, publishd by Epsilon-Uitgaven, 1987" -- T.p. verso

内容説明・目次

内容説明

This small book, translated into English for the first time, has long been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating, and the author provides many thought-provoking ideas.

目次

• The Pythagorean Theorem.- Ceva#x02019
• s Theorem.- Perpendicular Bisectors
• Concurrence.- The Nine-Point Circle and Euler Line.- The Taylor Circle.- Coordinate Systems with Respect to a Triangle.- The Area of a Triangle as a Function of the Barycentric Coordinates of Its Vertices.- The Distances from a Point to the Vertices of a Triangle.- The Simson Line.- Morley#x02019
• s Triangle.- Inequalities in a Triangle.- The Mixed Area of Two Parallel Polygons.- The Isoperimetric Inequality.- Poncelet Polygons.- A Closure Problem for Triangles.- A Class of Special Triangles.- Two Unusual Conditions for a Triangle.- A Counterpart for the Euler Line.- Menelaus#x02019
• s Theorem
• Cross-Ratios and Reciprocation.- The Theorems of Desargues, Pappus, and Pascal.- Inversion.- The Theorems of Ptolemy and Casey.- Pedal Triangles
• Brocard Points.- Isogonal Conjugation
• the Symmedian Point.- Isotomic Conjugation.- Triangles with Two Equal Angle Bisectors.- The Inscribed Triangle with the Smallest Perimeter
• the Fermat Point.

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詳細情報

• NII書誌ID(NCID): BA87232406
• ISBN:
  • 9780387781303
• LCCN: 2008931335
• 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
• 原本言語コード: dut
• 出版地: New York
• ページ数/冊数: xii, 142 p.
• 大きさ: 24 cm