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## Current revision as of 12:31, 1 July 2010

## Bibliographical Data

Title: | Lectures on Discrete and Polyhedral Geometry |

Author: | Igor Pak |

Subjects: | Mathematics |

Key words: | Polyhedral Geometry, Geometry, Discrete Mathematics |

Education Level: | Higher Education |

License: | All Rights Reserved - Standard Copyright |

Description: | Table of Contents
Part I. Basic Discrete Geometry 1. The Helly theorem 2. Carathéodory and Bárány theorems 3. The Borsuk conjecture 4. Fair division 5. Inscribed and circumscribed polygons 6. Dyson and Kakutani theorems 7. Geometric inequalities 8. Combinatorics of convex polytopes 9. Center of mass, billiards and the variational principle 10. Geodesics and quasi-geodesics 11. The Steinitz theorem and its extensions 12. Universality of point and line configurations 13. Universality of linkages 14. Triangulations 15. Hilbert's third problem 16. Polytope algebra 17. Dissections and valuations 18. Monge problem for polytopes 19. Regular polytopes 20. Kissing numbers Part II. Discrete Geometry of Curves and Surfaces 21. The four vertex theorem 22. Relative geometry of convex polygons 23. Global invariants of curves 24. Geometry of space curves 25. Geometry of convex polyhedra: basic results 26. Cauchy theorem: the statement, the proof and the story 27. Cauchy theorem: extensions and generalizations 28. Mean curvature and Pogorelov's lemma 29. Senkin-Zalgaller's proof of the Cauchy theorem 30. Flexible polyhedra 31. The algebraic approach 32. Static rigidity 33. Infinitesimal rigidity 34. Proof of the bellows conjecture 35. The Alexandrov curvature theorem 36. The Minkowski theorem 37. The Alexandrov existence theorem 38. Bendable surfaces 39. Volume change under bending 40. Foldings and unfoldings |

## Download

URL: | http://www.math.ucla.edu/~pak/book.htm |

Download link: | http://www.math.ucla.edu/~pak/geompol8.pdf |

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