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- 464 pages
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Discrete Geometry
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About This Book
Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analy
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Table of contents
- Cover
- Half Title
- Title Page
- Copyright Page
- Table of Contents
- Preface
- List of Contributors
- Biographical Notes and Work of W. Kuperberg
- 1. Transversal Lines to Lines and Intervals
- 2. On a Shortest Path Problem of G. Fejes Toth
- 3. A Short Survey of (r,q)-Structures
- 4. Lattice Points on the Boundary of the Integer Hull
- 5. The Erdös-Szekeres Problem for Planar Points in Arbitrary Position
- 6. Separation in Totally-Sewn 4-Polytopes
- 7. On a Class of Equifacetted Polytopes
- 8. Chessboard Ramsey Numbers
- 9. Maximal Primitive Fixing Systems for Convex Figures
- 10. The Newton-Gregory Problem Revisited
- 11. Arrangements of 13 Points on a Sphere
- 12. On Point Sets Without k Collinear Points
- 13. The Beckman-Quarles Theorem for Rational D-Spaces, D Even and D â„ 6
- 14. Edge-Antipodal Convex Polytopes - a Proof of Talata's Conjecture
- 15. Single-Split Tilings of the Sphere with Right Triangles
- 16. Vertex-Unfoldings of Simplicial Manifolds
- 17. View-Obstruction through Trajectories of Co-Dimension three
- 18. Fat 4-Polytopes and Fatter 3-Spheres
- 19. Arbitrarily Large Neighborly Families of Congruent Symmetric Convex 3-Polytopes
- 20. On the Non-Solidity of Some Packings and Coverings with Circles
- 21. On the mth Petty Numbers of Normed Spaces
- 22. Cubic Polyhedra
- 23. "New" Uniform Polyhedra
- 24. On the Existence of a Convex Polygon with a Specified Number of Interior Points
- 25. On-Line 2-Adic Covering of the Unit Square by Boxes
- 26. An Example of a Stable, Even Order Quadrangle Which is Determined by its Angle Function
- 27. Sets With a Unique Extension to a Set of Constant Width
- 28. The Number of Simplices Embracing the Origin
- 29. Helly-Type Theorems on Definite Supporting Lines for k-Disjoint Families of Convex Bodies in the Plane
- 30. Combinatorial Aperiodicity of Polyhedral Prototiles
- 31. Sequences of Smoothed Polygons
- 32. On a Packing Inequality by Graham,Witsenhausen and Zassenhaus
- 33. Covering a Triangle with Homothetic Copies
- 34. Open Problems
- Index