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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.
Jan Aarts is Professor Emeritus of Mathematics at Delft University of Technology. He is the Managing Director of the Dutch Masters Program of Mathematics.
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From the reviews:
"The book contains excellent illustrative diagrams, a reasonable selection of exercises, clear exposition, and fair number of worked examples and proofs, and a superb index. ... I found the book delightful. ... If you love Euclidean geometry you will certainly appreciate this book as part of your collection. The book would also make an excellent text for those in physics, chemistry that deal with crystallography, and other practical aspects of Euclidean geometry." (Collin Carbno, The Mathematical Association of America, July, 2009)
"This book is a masterful presentation of both plane and solid geometry. ... Aarts emphasizes mathematical proof throughout the presentation, not only to justify various properties but to also enhance insight. The numerous problems ... are frequently challenging and will be of interest to both beginning students and readers with a strong mathematical background. Readability is enhanced by over 250 figures. The work concludes with ... a list of 75 references. Summing Up: Recommended. Professional and academic readers, lower-division undergraduate and above." (D. P. Turner, Choice, Vol. 46 (11), July, 2009)
"The book contains excellent illustrative diagrams, a reasonable selection of exercises, clear exposition, and fair number of worked examples and proofs, and a superb index. ... I found the book delightful. ... If you love Euclidean geometry you will certainly appreciate this book as part of your collection. The book would also make an excellent text for those in physics, chemistry that deal with crystallography, and other practical aspects of Euclidean geometry." (Collin Carbno, The Mathematical Association of America, July, 2009)
"This book is a masterful presentation of both plane and solid geometry. ... Aarts emphasizes mathematical proof throughout the presentation, not only to justify various properties but to also enhance insight. The numerous problems ... are frequently challenging and will be of interest to both beginning students and readers with a strong mathematical background. Readability is enhanced by over 250 figures. The work concludes with ... a list of 75 references. Summing Up: Recommended. Professional and academic readers, lower-division undergraduate and above." (D. P. Turner, Choice, Vol. 46 (11), July, 2009)