Topics in Elementary Geometry

Paperback | August 20, 2008

byO. BottemaTranslated byReinie ErneForeword byRobin Hartshorne

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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.From the reviews:"This highly entertaining book will broaden the reader's historical perspective in an enlightening manner and it provides attractive topics for classroom discussion." - Hendrick Lenstra, University of Leiden"I think it would be a great addition to the books currently available in English." - Robin Hartshorne, University of California, Berkeley

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From the Publisher

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 y...

From the Jacket

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 y...

Format:PaperbackDimensions:154 pages, 9.25 × 6.1 × 0 inPublished:August 20, 2008Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387781307

ISBN - 13:9780387781303

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Table of Contents

Preface.- The Pythagorean theorem.- Ceva'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's triangle.- Inequalities in a triangle.- The Mixed area of two parallel polygons.- The Isoperimetric inequaltiy.- 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'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.- Appendix: remarks and hints.- References.- Index.-

Editorial Reviews

From the reviews of the second edition:"This small book includes Ceva's and Menelaus's theorems, the nine-point circle and Euler line, configuration theorems, Morley's triangle, inequalities for elements in a triangle . . The arguments are not only geometric or trigonometric ones but also different coordinate systems are considered such as barycentric or trilinear coordinates in relation to a given triangle. . The book is very useful for teachers and teacher students who want to be inspired by the results of elementary geometry." (Herbert Hotje, Zentralblatt MATH, Vol. 1159, 2009)