Geometric Constructions

Buch | Hardcover
206 Seiten
1997
Springer-Verlag New York Inc.
978-0-387-98276-2 (ISBN)

Lese- und Medienproben

Geometric Constructions - George E. Martin
69,54 inkl. MwSt
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.

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.

Erscheint lt. Verlag 5.12.1997
Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo XI, 206 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-387-98276-0 / 0387982760
ISBN-13 978-0-387-98276-2 / 9780387982762
Zustand Neuware
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