SOME UNSOLVED PROBLEMS CONCERNING CONVEX BODIES,

Abstract

The document contains five unrelated articles, each providing an exposition of certain unsolved problems concerning convex bodies. The titles of the five articles are as follows: 'Is a body spherical if its HA-measurements are constant', 'What is the expected volume of a simplex whose vertices are chosen at random from a given convex body', 'Can the boundary of a d-dimensional convex body contain segments in all directions', 'What are the intersection graphs of arcs in a circle', and 'What is the maximum length of a d-dimensional snake.' The problem of the first article is related to solid-state physics, of the second to the analysis of multicomponent phase diagrams, of the to approximation theory, of the fourth to molecular genetics, and of the fifth to the design of analog-to-digital conversion systems. These relationships are described in the articles.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1969
Accession Number
AD0696970

Entities

People

  • Victor Klee

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Bodies
  • Boundaries
  • Conversion
  • Convex Bodies
  • Diagrams
  • Genetics
  • Measurement
  • Molecular Genetics
  • Phase
  • Phase Diagrams
  • Physics
  • Solid State Physics

Readers

  • Graph Algorithms and Convex Optimization.
  • Materials Science and Engineering.
  • Political Science/ International Relations/ European Studies

Technology Areas

  • Biotechnology