Famous Problems of Geometry and how to Solve ThemEach chapter devoted to single type of problem with accompanying commentary and set of practice problems. Amateur puzzlists, students of mathematics and geometry will enjoy this rare opportunity to match wits with civilization s great mathematicians and witness the invention of modern mathemat" |
Contents
Achievement of the Ancient Greeks | 1 |
An Analytic Criterion for Constructibility | 7 |
Complex Numbers | 19 |
The Delian Problem | 29 |
The Problem of Trisecting an Angle | 33 |
The Problem of Squaring the Circle | 39 |
The Problem of Constructing Regular Polygons | 49 |
Concluding Remarks | 73 |
Suggestions for Further Reading | 81 |
Solutions to the Problems | 85 |
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17 sides 9 sides a₁ Available in U.S. Captions century coefficients complex numbers construct a regular construct a square construct regular polygons constructed with straight Continued Fractions cos³ cube cubic equation cyclotomic equation decimal divides edge and compasses equal in area equation of degree equation x² extractions of real F₁ Fermat finite number formula Gauss geometric given elements Greek mathematicians GUSTAV STICKLEY illustrations integers intersection k₁ Martin Gardner Moivre's theorem nth roots number in F number of rational obtain P₁ photographs polygon of 9 prime number PROBLEM SET proved quadratic equation quadratrix R₁ radius rational numbers rational operations rational root real numbers real square roots regular polygon root of x³ roots of unity solution solved square equal squaring the circle straight edge tions triangle trisecting an angle unit circle unmarked straight edge v₁ w₁ x₁ y₁ y₂ z₁ Απ