Ruler and the Round

Classic Problems in Geometric

Nicholas D. Kazarinoff

138 pages, parution le 15/05/2003

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Résumé

A number of geometric constructions, although easy to comprehend and fun to do, are nevertheless impossible to complete with just a ruler and a compass. This book discusses the most famous of these "impossible" constructions.
Part I, in exploring ground rules, history and angle trisection, considers--among other subjects--angle trisection and bird migration, constructed points, analytic geometry, algebraic classification of constructible numbers, fields of real numbers, cubic equations, and marked ruler, quadratrix, and hyperbola.
Part II treats nonconstructible regular polygons and the algebra associated with them, specifically, irreducibility and factorization, unique factorization of quadratic integers, finite dimensional vector spaces, algebraic fields, and nonconstructible regular polygons.
This stimulating and provocative book provides a fascinating glimpse of the crucial role geometry can play in a wide range of mathematical applications.
Unabridged republication of Ruler and the Round: or Angle Trisection and Circle Division, originally published by Prindle, Weber & Schmidt, Inc., Boston, 1970.

Contents

Angle Trisection

Proof and unsolved problems
Ground Rules and their Algebraic Interpretation
Some History
Fields
Angles, Cubes and Cubics
Other Means

Circle Division

Irreductibility and Factorization
Unique Factorization of Quadratic Itegers
Finite Dimensional Vector Spaces
Algebraic Fields
Nonconstructible Regular Polygons

Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	Nicholas D. Kazarinoff
Parution	15/05/2003
Nb. de pages	138
Format	13,5 x 21,5
Couverture	Broché
Poids	175g
Intérieur	Noir et Blanc
EAN13	9780486425153
ISBN13	978-0-486-42515-3