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Tables of Contents for Proofs from the Book
Chapter/Section Title
Page #
Page Count
Number Theory
1
36
Six proofs of the infinity of primes
3
4
Bertrand's postulate
7
6
Binomial coefficients are (almost) never powers
13
4
Representing numbers as sums of two squares
17
6
Every finite division ring is a field
23
4
Some irrational numbers
27
10
Geometry
37
48
Hilbert's third problem: decomposing polyhedra
39
8
Lines in the plane and decompositions of graphs
47
6
The slope problem
53
6
Three applications of Euler's formula
59
6
Cauchy's rigidity theorem
65
4
Touching simplices
69
4
Every large point set has an obtuse angle
73
6
Borsuk's conjecture
79
6
Analysis
85
44
Sets, functions, and the continuum hypothesis
87
12
In praise of inequalities
99
8
A theorem of Polya on polynomials
107
8
On a lemma of Littlewood and Offord
115
4
Cotangent and the Herglotz trick
119
6
Buffon's needle problem
125
4
Combinatorics
129
44
Pigeon-hole and double counting
131
12
Three famous theorems on finite sets
143
6
Lattice paths and determinants
149
6
Cayley's formula for the number of trees
155
6
Completing Latin squares
161
6
The Dinitz problem
167
6
Graph Theory
173
39
Five-coloring plane graphs
175
4
How to guard a museum
179
4
Turan's graph theorem
183
6
Communicating without errors
189
10
Of friends and politicians
199
4
Probability makes counting (sometimes) easy
203
9
About the Illustrations
212
1
Index
213