Strange Phenomena in Convex and Discrete Geometry

1. Front Matter

   Pages i-x

   PDF

2. Borsuk’s Problem

   • Chuanming Zong, James J. Dudziak

   Pages 1-13

3. Finite Packing Problems

   • Chuanming Zong, James J. Dudziak

   Pages 15-35

4. The Venkov-McMullen Theorem and Stein’s Phenomenon

   • Chuanming Zong, James J. Dudziak

   Pages 37-54

5. Local Packing Phenomena

   • Chuanming Zong, James J. Dudziak

   Pages 55-82

6. Category Phenomena

   • Chuanming Zong, James J. Dudziak

   Pages 83-98

7. The Busemann-Petty Problem

   • Chuanming Zong, James J. Dudziak

   Pages 99-122

8. Dvoretzky’s Theorem

   • Chuanming Zong, James J. Dudziak

   Pages 123-142

9. Back Matter

   Pages 143-158

   PDF

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

• Area
• Finite
• Lattice
• Lemma
• Partition
• Volume
• approximation
• boundary element method
• discrete geometry
• functions
• integral
• mathematics
• proof
• theorem
• training

• Department of Mathematics, Bucknell University, Lewisburg, USA

  James J. Dudziak

• Institute of Mathematics, The Chinese Academy of Sciences, Beijing, PR China

  Chuanming Zong

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