Topics in Elementary Geometry
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BeschreibungThis 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.
InhaltsverzeichnisPreface.- 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.-
PressestimmenFrom 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)
Untertitel: Revised. Sprache: Englisch.
Verlag: SPRINGER VERLAG GMBH
Erscheinungsdatum: August 2008
Seitenanzahl: 142 Seiten
Übersetzer/Sprecher: Übersetzt von Reinie Erne