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.
"This highly entertaining book will broaden the reader's historical perspective in an enlightening manner and it provides attractive topics for classroom discussion." -Hendrik Lenstra, Universiteit Leiden
Author(s): O. Bottema (auth.)
Edition: 2
Publisher: Springer-Verlag New York
Year: 2008
Language: English
Pages: 142
Tags: Geometry
Front Matter....Pages 1-8
The Pythagorean Theorem....Pages 1-6
Ceva’s Theorem....Pages 1-5
Perpendicular Bisectors; Concurrence....Pages 1-6
The Nine-Point Circle and Euler Line....Pages 1-3
The Taylor Circle....Pages 1-2
Coordinate Systems with Respect to a Triangle....Pages 1-4
The Area of a Triangle as a Function of the Barycentric Coordinates of Its Vertices....Pages 1-4
The Distances from a Point to the Vertices of a Triangle....Pages 1-5
The Simson Line....Pages 1-3
Morley’s Triangle....Pages 1-3
Inequalities in a Triangle....Pages 1-4
The Mixed Area of Two Parallel Polygons....Pages 1-5
The Isoperimetric Inequality....Pages 1-7
Poncelet Polygons....Pages 1-7
A Closure Problem for Triangles....Pages 1-3
A Class of Special Triangles....Pages 1-4
Two Unusual Conditions for a Triangle....Pages 1-2
A Counterpart for the Euler Line....Pages 1-2
Menelaus’s Theorem; Cross-Ratios and Reciprocation....Pages 1-5
The Theorems of Desargues, Pappus, and Pascal....Pages 1-7
Inversion....Pages 1-3
The Theorems of Ptolemy and Casey....Pages 1-4
Pedal Triangles; Brocard Points....Pages 1-4
Isogonal Conjugation; the Symmedian Point....Pages 1-5
Isotomic Conjugation....Pages 1-2
Triangles with Two Equal Angle Bisectors....Pages 1-3
The Inscribed Triangle with the Smallest Perimeter; the Fermat Point....Pages 1-3
Back Matter....Pages 1-15
