Topics in elementary geometry
"This small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which...
| Uniform Title: | Hoofdstukken uit de elementaire meekunde. English |
|---|---|
| Main Author: | Bottema, O. |
| Other Authors: | SpringerLink (Online Service) |
| Format: | eBook |
| Language: | English Dutch |
| Published: |
New York :
Springer,
©2008.
|
| Physical Description: |
1 online resource (xii, 142 pages) : illustrations. |
| Edition: | 2nd ed. / |
| Subjects: |
| Summary: |
"This small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained in this classical field 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. In a small space the author provides many thought-provoking ideas. This book will fit in well with the increasing interest for geometry in research and education. This book was originally published in Dutch, and this will be the first English translation. This translation also includes a new foreword by Robin Hartshorne."--Jacket. |
|---|---|
| Item Description: |
Includes bibliographical references (pages 133-137) and index. Translated from the Dutch. "This small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained in this classical field 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. In a small space the author provides many thought-provoking ideas. This book will fit in well with the increasing interest for geometry in research and education. This book was originally published in Dutch, and this will be the first English translation. This translation also includes a new foreword by Robin Hartshorne."--Jacket. Machine derived contents note: 1 The Pythagorean Theorem 1 -- 2 Ceva's Theorem 7 -- 3 Perpendicular Bisectors; Concurrence 13 -- 4 The Nine-Point Circle and Euler Line 19 -- 5 The Taylor Circle 23 -- 6 Coordinate Systems with Respect to a Triangle 25 -- 7 The Area of a Triangle as a Function of the Barycentric -- Coordinates of Its Vertices 29 -- 8 The Distances from a Point to the Vertices of a Triangle 33 -- 9 The Simson Line 39 -- 10 Morley's Triangle 43 -- 11 Inequalities in a Triangle 47 -- 12 The Mixed Area of Two Parallel Polygons 51 -- 13 The Isoperimetric Inequality. 57 -- 14 Poncelet Polygons 65 -- 15 A Closure Problem for Triangles 73 -- 16 A Class of Special Triangles 77 -- 17 Two Unusual Conditions for a Triangle 81 -- 18 A Counterpart for the Euler Line 83 -- 19 Menelaus's Theorem; Cross-Ratios and Reciprocation 85 -- 20 The Theorems of Desargues, Pappus, and Pascal 91 -- 21 Inversion 99 -- 22 The Theorems of Ptolemy and Chsey 103 -- 23 Pedal Triangles; Brocard Points 107 -- 24 Isogonal Conjugation; the Symmedian Point 111 -- 25 Isotomic Conjugation 117 -- 26 Triangles with Two Equal Angle Bisectors 119 -- 27 The Inscribed Triangle with the Smallest Perimeter; the -- Fermat Point 123. University staff and students only. Requires University Computer Account login off-campus. |
| Physical Description: |
1 online resource (xii, 142 pages) : illustrations. |
| Bibliography: |
Includes bibliographical references (pages 133-137) and index. |
| ISBN: |
9780387781310 0387781315 |
| Access: |
University staff and students only. Requires University Computer Account login off-campus. |