Proofs from THE BOOK

Table of Contents

    Number Theory

  1. Six proofs of the infinity of primes
  2. Bertrand's postulate
  3. Binomial coefficients are (almost) never powers
  4. Representing numbers as sums of two squares
  5. Every finite division ring is a field
  6. Some irrational numbers

    Geometry

  7. Hilbert's third problem: decomposing polyhedra
  8. Lines in the plane and decompositions of graphs
  9. The slope problem
  10. Three applications of Euler's formula
  11. Cauchy's rigidity theorem
  12. The problem of the thirteen spheres
  13. Touching simplices
  14. Every large point set has an obtuse angle
  15. Borsuk's conjecture

    Analysis

  16. Sets, functions, and the continuum hypothesis
  17. In praise of inequalities
  18. A theorem of Pólya on polynomials
  19. On a lemma of Littlewood and Offord

    Combinatorics

  20. Pigeon-hole and double counting
  21. Three famous theorems on finite sets
  22. Cayley's formula for the number of trees
  23. Completing Latin squares
  24. The Dinitz problem

    Graph Theory

  25. Five-coloring plane graphs
  26. How to guard a museum
  27. Turán's graph theorem
  28. Communicating without errors
  29. Of friends and politicians
  30. Probability makes counting (sometimes) easy

About the Illustrations

Index

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Copyright © 1996-2018 Alexander Bogomolny

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