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Other titles in the Undergraduate Texts in Mathematics series:
Geometric Constructions (Undergraduate Texts in Mathematics)by George Edward Martin
Synopses & ReviewsPublisher Comments: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.
Synopsis:Written in an informal style that intersperses history and philosophy with mathematics, this classtested, selfcontained book demonstrates how some simple construction tools can be associated with various fields of real numbers through coordinate geometry.
Synopsis: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.
Description:Includes bibliographical references (p. [189]197) and index.
Table of ContentsEuclidean Constructions. The Ruler and Compass. The Compass and the MohrMascheroni Theorem. The Ruler. The Ruler and Dividers. The PonceletSteiner Theorem and Double Rulers. The Ruler and Rusty Compass. Sticks. The Marked Ruler. Paperfolding  The Back of the Book.
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