Geometry: Plane and Fancy

Geometry: Plane and Fancy

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A fascinating tour through parts of geometry students are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclids fifth postulate lead to interesting and different patterns and symmetries, and, in the process of examining geometric objects, the author incorporates the algebra of complex and hypercomplex numbers, some graph theory, and some topology. Interesting problems are scattered throughout the text. Nevertheless, the book merely assumes a course in Euclidean geometry at high school level. While many concepts introduced are advanced, the mathematical techniques are not. Singers lively exposition and off-beat approach will greatly appeal both to students and mathematicians, and the contents of the book can be covered in a one-semester course, perhaps as a sequel to a Euclidean geometry course.This means that the interior angle of the polygon has to divide 360Ad evenly. Leta#39;s compute the interior angles of an n-gon. ... Let the dihedral group D4 (see the last section) be the group of isometries that take the home square to itself; thenanbsp;...

Title:Geometry: Plane and Fancy
Author: David A. Singer
Publisher:Springer Science & Business Media - 2012-12-06

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