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Ruler and the Round Classic Problems in Geometric Constructions

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ISBN-10: 0486425150

ISBN-13: 9780486425153

Edition: 2002 (Unabridged)

Authors: Nicholas D. Kazarinoff

List price: $10.95
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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.
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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
Solved and Unsolved Problems
Things to Come
Ground Rules and Their Algebraic Interpretation
Constructed Points
Analytic Geometry
Some History
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