Accession Number : AD0710642

Title :   TOLERANCE GEOMETRY,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Roberts,Fred S.

Report Date : AUG 1970

Pagination or Media Count : 23

Abstract : In his work on visual perception, Zeeman points out that any model of perception must take account of the fact that one cannot distinguish between points that are sufficiently close. A similar observation has been made for choice behavior by Luce. This observation suggests that in order to study perception and9choice behavior, it is necessary to replace classical geometrical primitives, such as betweeness, straightness, perpendicularity, parallelism, etc., with more general notions, obtained from the classical ones by substituting closeness for identity. The term tolerance geometry is used for any geometry whose primitives are obtained by such a perturbation. This paper gives axioms for tolerance geometry on the line, where the classical ternary relation of betweeness is replaced by the tolerance relation of epsilon-betweeness. In particular, these axioms are stated in terms of a pair (A, B) where A is a finite set and B is a ternary relation on A (epsilon-betweeness). (Author)

Descriptors :   (*VISUAL PERCEPTION, *GEOMETRY), PERFORMANCE(HUMANS), TOLERANCES(PHYSIOLOGY), GROUPS(MATHEMATICS), GRAPHICS, THEOREMS

Subject Categories : Anatomy and Physiology
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE