SOME PROBLEMS INVOLVING CIRCULAR AND SPHERICAL TARGETS

Abstract

This article is concerned with some problems which occur in certain tactical considerations: how should one place k circles (spheres) in the plane (3-space) so that their union has the greatest standard normal probability measure, that is, so as to maximize the probability that a random normal point will fall in one or more of the circles (spheres). For k > 3 the problem seems hopeless, (except for certain special situations); the case for k = 3 is still unresolved and is being worked on by a number of investigators, and the case for k = 2 is solved completely in this paper. The results for k = 2 have some practical value when applied to actual problems arising in tactical considerations, and some theoretical value, as a method of attacking the problem for k > 3.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1964
Accession Number
AD0600566

Entities

People

  • George Marsaglia

Organizations

  • Boeing

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Approximation (Mathematics)
  • Equations
  • Integrals
  • Mathematics
  • Nomographs
  • Normal Distribution
  • Probability
  • Scientific Research
  • Standards
  • Thickness

Fields of Study

  • Mathematics

Readers

  • Statistical inference.
  • Systems Analysis and Design

Technology Areas

  • Space
  • Space - Orbital Debris