Ruler and the Round Classic Problems in Geometric Constructions

Name: Ruler and the Round Classic Problems in Geometric Constructions
Price: 6.73 USD
Availability: InStock
ISBN: 9780486425153

ISBN-10: 0486425150

ISBN-13: 9780486425153

Edition: 2002 (Unabridged)

Authors: Nicholas D. Kazarinoff

List price: $10.95

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Description:

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 duscusses the most famous of these impossible constructions.

Book details

List price: $10.95
Copyright year: 2002
Publisher: Dover Publications, Incorporated
Publication date: 10/20/2011
Binding: Paperback
Pages: 160
Size: 5.25" wide x 8.25" long x 0.50" tall
Weight: 0.396
Language: English




Angle Trisection



Proof and Unsolved Problems



Angle Trisection and Bird Migration



Proof



Solved and Unsolved Problems



Things to Come



Ground Rules and Their Algebraic Interpretation



Constructed Points



Analytic Geometry



Some History



Fields



Fields of Real Numbers



Quadratic Fields



Iterated Quadratic Extensions of R



Algebraic Classification of Constructible Numbers



Angles, Cubes, and Cubics



Cubic Equations



Angles of 20[degree]



Doubling a Unit Cube



Some Trisectable and Nontrisectable Angles



Trisection with n Points Given



Other Means



Marked Ruler, Quadratrix, and Hyperbola



Approximate Trisections



Circle Division



Irreducibility and Factorization



Why Irreducibility?



Unique Factorization



Eisenstein's Test



Unique Factorization of Quadratic Integers



Finite Dimensional Vector Spaces



Definitions and Examples



Linear Dependence and Linear Independence



Bases and Dimension



Bases for Iterated Quadratic Extensions of R



Algebraic Fields



Algebraic Fields as Vector Spaces



The Last Link



Nonconstructible Regular Polygons



Construction of a Regular Pentagon



Constructibility of Regular Pentagons, a Second View



Irreducible Polynomials and Regular (2n + 1)-gons



Nonconstructible Regular Polygons



Regular p[superscript n]-gons



Squaring a Circle


Appendix I


Appendix II


References


Index