GEOGRAPHY AND THE PROPERTIES OF SURFACES. THE DETERMINATION OF FIXED-POINTS IN FINITE-DIMENSIONAL SPACES.

Abstract

L.E.J. Brouwer's fixed-point theorem proves the existence of a fixed-point in a finite-dimensional space which is both convex and bounded, but provides no means of determining its position. For the case of a one-dimensional space, Marvin Shinbrot uses a graphical solution which can also be accepted as a proof for the theorem. This paper extends Shinbrot's solution to any number of dimensions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 03, 1970
Accession Number
AD0707771

Entities

People

  • C. Ernesto S. Lindgren

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Earth Sciences
  • Geography
  • Geometry
  • Interdisciplinary Science
  • Mathematics
  • Planetary Sciences
  • Point Theorem

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Small Business Innovation Research Program (SBIR) EDI Research and Innovation.

Technology Areas

  • Space