Elementary Geometry (Student Mathematical Library)

by Ilka Agricola and Thomas Friedrich

Elementary geometry provides the foundation of modern geometry. For the most part, the standard introductions end at the formal Euclidean geometry of high school. Agricola and Friedrich revisit geometry, but from the higher viewpoint of university mathematics. Plane geometry is developed from its basic objects and their properties and then moves to conics and basic solids, including the Platonic solids and a proof of Euler's polytope formula. Particular care is taken to explain symmetry groups, including the description of ornaments and the classification of isometries by their number of fixed points. Complex numbers are introduced to provide an alternative, very elegant approach to plane geometry. The authors then treat spherical and hyperbolic geometries, with special emphasis on their basic geometric properties. This largely self-contained book provides a much deeper understanding of familiar topics, as well as an introduction to new topics that complete the picture of two-dimensional geometries. For undergraduate mathematics students the book will be an excellent introduction to an advanced point of view on geometry. For mathematics teachers it will be a valuable reference and a source book for topics for projects. The book contains over 100 figures and scores of exercises. It is suitable for a one-semester course in geometry for undergraduates, particularly for mathematics majors and future secondary school teachers.

243 pages, Paperback

First published February 29, 2008

Reviews

[Thomas Bell · Rating 1 out of 5]

This is a terrible book. Explanations aren't that great, and neither is the translation. For a simple example, we call it a cube - not a hexahedron.

And the book assumes that all my poor students have had classes in EVERY field of undergraduate mathematics, including abstract algebra, multi-variable calculus, topology and differential equations. Then the problems are WAY too difficult for a standard undergraduate math major. Some of the problems took me, a professor, many hours to complete. Others took me many hours to even figure out what the devil the authors were asking. Granted, there were only about 100 problems in the book, but they were too difficult for my poor students. I will never use this book again.

I had a tex file with all the solutions, but alas I must have overridden the file with solutions to problems in better books.