Customer Reviews

Geometric Constructions (Undergraduate Texts in Mathematics)

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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.

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.

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.