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  • Geometric Constructions (Undergraduate Texts in Mathematics)

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Geometric Constructions (Undergraduate Texts in Mathematics)

by George E. Martin (Author) Format: Hardcover
3.8 out of 5 stars (7)
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Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations. As specified by Plato, the game is played with a ruler and compass. The first chapter is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never seen. The second chapter formalizes Plato's game and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, using only a compass, using toothpicks, using a ruler and dividers, using a marked rule, using a tomahawk, and ending with a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics. He hopes that readers will learn a little geometry and a little algebra while enjoying the effort. This is as much an algebra book as it is a geometry book. Since all the algebra and all the geometry that are needed is developed within the text, very little mathematical background is required to read this book. This text has been class tested for several semesters with a master's level class for secondary teachers.
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  1. ISBN-10
    0387982760
  2. ISBN-13
    978-0387982762
  3. Edition
    1998th
  4. Publisher
    Springer
  5. Publication date
    December 5, 1997
  6. Part of series
    Undergraduate Texts in Mathematics
  7. Language
    English
  8. Dimensions
    6.3 x 0.61 x 9.44 inches
  9. Print length
    217 pages
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Product details

  • Publisher ‏ : ‎ Springer
  • Publication date ‏ : ‎ December 5, 1997
  • Edition ‏ : ‎ 1998th
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 217 pages
  • ISBN-10 ‏ : ‎ 0387982760
  • ISBN-13 ‏ : ‎ 978-0387982762
  • Item Weight ‏ : ‎ 1 pounds
  • Dimensions ‏ : ‎ 6.3 x 0.61 x 9.44 inches
  • Part of series ‏ : ‎ Undergraduate Texts in Mathematics
  • Best Sellers Rank: #465,315 in Books (See Top 100 in Books)
  • Customer Reviews:
    3.8 out of 5 stars (7)

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George Edward Martin

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Customer reviews

3.8 out of 5 stars
7 global ratings
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Top reviews from the United States

  • Craig Matteson
    5 out of 5 stars
    I wish I could give it more than five stars - a delight!
    Reviewed in the United States on July 12, 2004
    Format: Hardcover
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    Full content visible, double tap to read brief content.

    This is a magical book. It took me a long time to find it, but I am glad that I did. I was never taught the nearly lost art of drawing geometrical figures with a straight edge and a compass. We did a tiny bit of paper folding in seventh grade, but I never really understood how to get to the core of the geometry.

    This brief book makes it all a delightful game with clear notation and a tremendously logical orientation. It makes it possible for anyone who has a desire to learn this topic to get a solid grounding that will help all their further studies in geometry by providing a foundation in the intuitions of how the geometric proof is actually made.

    I am so delighted to have found this book and recommend it to you highly.

    18 people found this helpful
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  • james Slayter
    4 out of 5 stars
    Lots of information in this one. I'm still trying ...
    Reviewed in the United States on March 31, 2015
    Format: Hardcover
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    Full content visible, double tap to read brief content.

    Lots of information in this one. I'm still trying to adsorb all of it. It fits well in my collection of math books.

    2 people found this helpful
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  • G. Allen
    2 out of 5 stars
    Very Abstract
    Reviewed in the United States on July 20, 2004
    Format: Hardcover
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    Full content visible, double tap to read brief content.

    The book starts off strong with a thorough review of Euclid's constructions complete with explanations of the constructions themselves. Things go down rapidly from there.

    Most of the remainder of the book is a very abstract discussion of constructability under various conditions. After the first chapter there are very few concrete constructions performed.

    If you're looking for a discussion of the theoretical basis of geometric constructions under a variety of conditions this book is an excellent resource. If you're looking for practical, step-by-step constructions that go beyond Euclid you should look elsewhere.

    14 people found this helpful
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  • Viktor Blasjo
    3 out of 5 stars
    Read Courant & Robbins instead
    Reviewed in the United States on March 25, 2007
    Format: Hardcover
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    I don't like this book. For example, the proof of the key theorem that any ruler-and-compass construction can be carried out with compass alone is 10 pages long and very tedious. There is a much clearer, completely different proof in Courant & Robbins. I find it odd and inexcusable that Martin doesn't even mention this accessible proof. It is true that it uses inversions and that the purest of the pure Euclideans might prefer to avoid it for this reason, but this excuse is not available to Martin since, for example, the proof of Steiner's theorem that any ruler-and-compass construction can be carried out with ruler and one given circle is a half-page analytic magic proof that will have classical geometers turning in their graves.

    10 people found this helpful
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Top reviews from other countries

  • Anna Cristina Pozzato
    2 out of 5 stars
    Not satisfactory
    Reviewed in the United Kingdom on April 24, 2013
    Format: Hardcover
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    I bought it hoping to find guidelines on how to use compass and ruler for exercises at the undergraduate level but it was too theoretical

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