Topics in Elementary Geometry / Edition 2 available in Paperback
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.
|Publisher:||Springer New York|
|Edition description:||2nd ed. 2008|
|Product dimensions:||6.10(w) x 9.25(h) x 0.36(d)|
Table of ContentsThe 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.