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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.

Mathematics. --- Geometry. --- Mathématiques --- Géométrie --- Electronic books. -- local. --- Geometry, Plane. --- Geometry, Solid. --- Geometry, Plane --- Geometry, Solid --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Solid geometry --- Plane geometry --- Euclid's Elements --- Math --- Science

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Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a s

Dimension theory (Topology) --- Mappings (Mathematics) --- Compactifications.