- Page 4 and 5: Martin Aigner Günter M. Ziegler Pr
- Page 6 and 7: Preface Paul Erdős liked to talk a
- Page 8 and 9: Table of Contents Number Theory 1 1
- Page 10: Number Theory 1 Six proofs of the i
- Page 13 and 14: 4 Six proofs of the infinity of pri
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- Page 17 and 18: 8 Bertrand’s postulate (2) Next w
- Page 19 and 20: 10 Bertrand’s postulate One can e
- Page 21 and 22: 12 Bertrand’s postulate 1 1 1 1 1
- Page 23 and 24: 14 Binomial coefficients are (almos
- Page 25 and 26: 16 Binomial coefficients are (almos
- Page 27 and 28: 18 Representing numbers as sums of
- Page 29 and 30: 20 Representing numbers as sums of
- Page 31 and 32: 22 Representing numbers as sums of
- Page 33 and 34: 24 The law of quadratic reciprocity
- Page 35 and 36: 26 The law of quadratic reciprocity
- Page 37 and 38: 28 The law of quadratic reciprocity
- Page 39 and 40: 30 The law of quadratic reciprocity
- Page 41 and 42: 32 Every finite division ring is a
- Page 43 and 44: 34 Every finite division ring is a
- Page 45 and 46: 36 Some irrational numbers Geometri
- Page 47 and 48: 38 Some irrational numbers where fo
- Page 49 and 50: 40 Some irrational numbers integral
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Three times π 2 /6 Chapter 8 We kn
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Three times π 2 /6 45 This proof e
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Three times π 2 /6 47 Comparison o
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Three times π 2 /6 49 Appendix: Th
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Geometry 9 Hilbert’s third proble
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54 Hilbert’s third problem: decom
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56 Hilbert’s third problem: decom
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58 Hilbert’s third problem: decom
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60 Hilbert’s third problem: decom
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Lines in the plane and decompositio
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Lines in the plane, and decompositi
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Lines in the plane, and decompositi
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70 The slope problem Three pretty s
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72 The slope problem is crossing of
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Three applications of Euler’s for
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Three applications of Euler’s for
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Three applications of Euler’s for
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Cauchy’s rigidity theorem Chapter
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Cauchy’s rigidity theorem 83 Now
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Touching simplices Chapter 14 How m
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Touching simplices 87 In contrast t
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Every large point set has an obtuse
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Every large point set has an obtuse
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Every large point set has an obtuse
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Borsuk’s conjecture Chapter 16 Ka
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Borsuk’s conjecture 97 (3) From R
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Borsuk’s conjecture 99 Claim 4. T
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Analysis 17 Sets, functions, and th
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104 Sets, functions, and the contin
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106 Sets, functions, and the contin
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108 Sets, functions, and the contin
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110 Sets, functions, and the contin
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112 Sets, functions, and the contin
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114 Sets, functions, and the contin
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116 Sets, functions, and the contin
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118 Sets, functions, and the contin
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120 In praise of inequalities For n
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122 In praise of inequalities We fi
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124 In praise of inequalities Apply
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The fundamental theorem of algebra
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The fundamental theorem of algebra
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132 One square and an odd number of
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134 One square and an odd number of
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136 One square and an odd number of
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138 One square and an odd number of
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140 A theorem of Pólya on polynomi
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142 A theorem of Pólya on polynomi
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144 A theorem of Pólya on polynomi
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146 On a lemma of Littlewood and Of
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148 On a lemma of Littlewood and Of
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150 Cotangent and the Herglotz tric
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152 Cotangent and the Herglotz tric
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154 Cotangent and the Herglotz tric
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156 Buffon’s needle problem If yo
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158 Buffon’s needle problem Refer
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Pigeon-hole and double counting Cha
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Pigeon-hole and double counting 163
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Pigeon-hole and double counting 165
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Pigeon-hole and double counting 167
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Pigeon-hole and double counting 169
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Pigeon-hole and double counting 171
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174 Tiling rectangles Since ∫ d
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176 Tiling rectangles Next comes a
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Three famous theorems on finite set
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Three famous theorems on finite set
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Three famous theorems on finite set
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186 Shuffling cards which is smalle
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188 Shuffling cards For card player
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190 Shuffling cards and we have see
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192 Shuffling cards Bell Labs “Ma
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194 Shuffling cards k d(k) 1 1.000
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196 Lattice paths and determinants
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198 Lattice paths and determinants
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200 Lattice paths and determinants
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202 Cayley’s formula for the numb
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204 Cayley’s formula for the numb
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206 Cayley’s formula for the numb
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208 Identities versus bijections th
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210 Identities versus bijections Eu
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212 Identities versus bijections Re
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214 Completing Latin squares 1 2 3
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216 Completing Latin squares Inequa
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218 Completing Latin squares In our
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The Dinitz problem Chapter 33 The f
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The Dinitz problem 223 To state our
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The Dinitz problem 225 Claim. When
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Five-coloring plane graphs Chapter
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Five-coloring plane graphs 229 For
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How to guard a museum Chapter 35 He
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How to guard a museum 233 convex ve
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Turán’s graph theorem Chapter 36
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Turán’s graph theorem 237 all ve
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Turán’s graph theorem 239 Case 2
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242 Communicating without errors se
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244 Communicating without errors by
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246 Communicating without errors No
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248 Communicating without errors
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250 Communicating without errors Re
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252 The chromatic number of Kneser
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254 The chromatic number of Kneser
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Of friends and politicians Chapter
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Of friends and politicians 259 Now
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262 Probability makes counting (som
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264 Probability makes counting (som
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266 Probability makes counting (som
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268 Probability makes counting (som
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About the Illustrations We are happ
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272 Index division ring, 31 double
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274 Index tangential rectangle, 121