Plane and Solid Geometry

ISBN-13: 9780387782409 / Angielski / Miękka / 2008 / 364 str.

J. M. Aarts

Opis

Nature and the world around us that we ourselves design, furnish, and build contain many geometric patterns and structures. This is one of the reasons that geometry should be studied at school. At ?rst, the study of geometry is experimental. Results are taught and used in numerous examples. Only later do proofs come into play. But are these proofs truly necessary, or can we do without them? A natural answer is that every statement must be provided with a proof, because we want to know whether it is true. However, it is clear that the less experienced student may become frustrated by the pr- ence of too many proofs. Only later will the student understand that proofs not only show the correctness of a statement, but also provide better insight into the relationsamong various propertiesof the objects that arebeing st- ied. Learning statements without proofs, you risk not being able to see the forest for the trees. For this reason, we will pay much attention to a careful presentation of proofs in this book. In the development of the theory of plane geometry there are, however, many tricky questions, especially at the beg- ning. The presentation of proofs at that stage is in general more concealing than revealing. My ?rst objective in writing this book has been to give an accessible - position of the most common notions and properties of elementary Euclidean geometry in dimensions two and three.

Recenzje

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)

Spis treści

Plane Geometry.- Transformations.- Symmetry.- Curves.- Solid Geometry.

Blurb

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.