Informazioni su questo prodotto

Product Identifiers

PublisherSpringer New York

ISBN-100387982760

ISBN-139780387982762

eBay Product ID (ePID)396341

Product Key Features

Number of PagesXi, 206 Pages

LanguageEnglish

Publication NameGeometric Constructions

SubjectGeometry / General

Publication Year1997

TypeTextbook

Subject AreaMathematics

AuthorGeorge E. Martin

SeriesUndergraduate Texts in Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.2 in

Item Weight38.4 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN97-022885

Dewey Edition21

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal516

Table Of Content1 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.

SynopsisThis is a text on geometric constructions--a popular area of mathematics since the time of Plato to the modern classroom. The author takes advantage of modern algebra and the resultant coordinate geometry to analyze and classify these problems. Various geometric construction tools are associated with various algebraic fields of numbers and elements of algebra are necessarily encountered while exploring the constructions., Written in an informal style that intersperses history and philosophy with mathematics, this class-tested, self-contained book demonstrates how some simple construction tools can be associated with various fields of real numbers through coordinate geometry., 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.

LC Classification NumberQA440-699