Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises 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, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
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Most Helpful Customer Reviews
10 of 10 people found the following review helpful:
5.0 out of 5 stars
I wish I could give it more than five stars - a delight!,
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This review is from: Geometric Constructions (Undergraduate Texts in Mathematics) (Hardcover)
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.
5 of 6 people found the following review helpful:
3.0 out of 5 stars
Read Courant & Robbins instead,
This review is from: Geometric Constructions (Undergraduate Texts in Mathematics) (Hardcover)
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.
7 of 14 people found the following review helpful:
2.0 out of 5 stars
Very Abstract,
This review is from: Geometric Constructions (Undergraduate Texts in Mathematics) (Hardcover)
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.
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