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Plane and Solid Geometry

  • Textbook
  • © 2008

Overview

Authors:
  1. J.M. Aarts
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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)

Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages 1-11
    Download chapter PDF

  2. Plane Geometry

    • J.M. Aarts, R. Erne
    Pages 1-36

  3. Transformations

    • J.M. Aarts, R. Erne
    Pages 1-58

  4. Symmetry

    • J.M. Aarts, R. Erne
    Pages 1-50

  5. Curves

    • J.M. Aarts, R. Erne
    Pages 1-109

  6. Solid Geometry

    • J.M. Aarts, R. Erne
    Pages 1-77

  7. Back Matter

    Pages 1-15
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Keywords

About this book

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.

Reviews

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)

Bibliographic Information

  • Book Title: Plane and Solid Geometry

  • Authors: J.M. Aarts

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-0-387-78241-6

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2008

  • Softcover ISBN: 978-0-387-78240-9Published: 08 October 2008

  • eBook ISBN: 978-0-387-78241-6Published: 28 April 2009

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 349

  • Number of Illustrations: 258 b/w illustrations

  • Topics: Geometry

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