Undergraduate Texts in Mathematics: Geometric Constructions (Hardback)
Undergraduate Texts in Mathematics: Geometric Constructions (Hardback)
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From the back cover: "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, suing 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 needed are developed within the text, very little mathematical background is required to read this book. The text has been class-tested for several semesters with a master's level class for secondary teachers."
BRIEF CONTENTS
- Preface
- 1. Euclidean Constructions
- 2. The Ruler and Compass
- 3. The Compass and the Mohr-Mascheroni Theorem
- 4. The Ruler
- 5. The Ruler and Dividers
- 6. The Poncelet-Steiner Theorem and Double Rulers
- 7. The Ruler and Rusty Compass
- 8. Sticks
- 9. The Marked Ruler
- 10. Paperfolding
- The Back of the Book
- Suggested Reading and References
- Index
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PUBLISHER: Springer-Verlag
ISBN-13: 9780387982762
ISBN-10: 0387982760