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Many unique topics are covered, such as fractals and cycloids
Author uses a non-traditional approach (he defines a right angle by using the Pythagorean Theorem)
Lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses
This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.
Jan Aarts is Professor Emeritus of Mathematics at Delft University of Technology. He is the Managing Director of the Dutch Masters Program of Mathematics.