دانلود کتاب Mathematical Surprises

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Foreword
Preface
What Is a Surprise?
An Overview of the Contents
Style
Acknowledgments
Contents
Chapter 1 The Collapsing Compass
1.1 Construction with a Straightedge and Compass
1.2 Fixed Compasses and Collapsing Compasses
1.3 Euclid’s Construction for Copying a Line Segment
1.4 A Flawed Construction for Copying a Line Segment
1.5 Don’t Trust a Diagram
What Is the Surprise?
Sources
Chapter 2 Trisection of an Angle
2.1 Approximate Trisections
2.1.1 First Approximate Trisection
2.1.2 Second Approximate Trisection
2.2 Trisection Using a Neusis
2.3 Doubling the Cube with a Neusis
2.4 Trisection Using a Quadratrix
2.5 Constructible Numbers
2.6 Constructible Numbers As Roots of Polynomials
2.7 Impossibility of the Classical Constructions
What Is the Surprise?
Sources
Chapter 3 Squaring the Circle
3.1 Kocha´nski’s Construction
3.2 Ramanujan’s First Construction
3.3 Ramanujan’s Second Construction
3.4 Squaring a Circle Using a Quadratrix
What Is the Surprise?
Sources
Chapter 4 The Five-Color Theorem
4.1 Planar Maps and Graphs
4.2 Euler’s Formula
4.3 Non-planar Graphs
4.4 The Degrees of the Vertices
4.5 The Six-Color Theorem
4.6 The Five-Color Theorem
4.7 Kempe’s Incorrect Proof of the Four-Color Theorem
What Is the Surprise?
Sources
Chapter 5 How to Guard a Museum
5.1 Coloring Triangulated Polygons
5.2 From Coloring of Polygons to Guarding a Museum
5.3 Any Polygon Can Be Triangulated
What Is the Surprise?
Sources
Chapter 6 Induction
6.1 The Axiom of Mathematical Induction
6.2 Fibonacci Numbers
6.3 Fermat Numbers
6.4 McCarthy’s 91-function
6.5 The Josephus Problem
What Is the Surprise?
Sources
Chapter 7 Solving Quadratic Equations
7.1 Traditional Methods for Solving Quadratic Equations
7.2 The Relation Between the Roots and the Coefficients
7.3 Examples of Loh’s Method
7.4 Derivation of the Traditional Formula
7.5 Al-Khwarizmi’s Geometric Solution of Quadratic Equations
7.6 Cardano’s Construction for Solving Cubic Equations
7.7 They Weren’t Intimidated by Imaginary Numbers
7.8 Lill’s Method and Carlyle’s Circle
7.9 Numerical Computation of the Roots
What Is the Surprise?
Sources
Chapter 8 Ramsey Theory
8.1 Schur triples
8.2 Pythagorean Triples
8.3 Van der Waerden’s problem
8.4 Ramsey’s Theorem
8.5 The Probabilistic Method
8.6 SAT Solving
8.6.1 Propositional Logic and the SAT Problem
8.6.2 Schur triples
8.6.3 Pythagorean Triples
8.6.4 An Overview of the DPLL Algorithm
8.7 Pythagorean Triples in Babylonian Mathematics
What Is the Surprise?
Sources
Chapter 9 Langford’s Problem
9.1 Langford’s Problem as a Covering Problem
9.2 For Which Values of