Accession Number : AD0763695

Title :   The Orchard Problem.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Burr,Stefan A. ; Gruenbaum,Branko ; Sloane,N. J. A.

Report Date : JUL 1973

Pagination or Media Count : 47

Abstract : The geometric version of the problem of Kirkman-Steiner triples may be formulated as follows: What is the maximal possible number t(p) of lines each of which contains precisely three points of a suitable set of p points in the Euclidean plane. The first general results were announced by J. J. Sylvester in 1867 and 1868, but up to now no proof of his best claims was published. The authors present a proof of a theorem improving those given by Sylvester, together with several related results. The general estimate they obtain may be put in the form (p(p-3)/6) + 1 < or = t(p) < or = (p(p-3)/6 + 4p/21). (Author)

Descriptors :   (*ANALYTIC GEOMETRY, THEOREMS), ALIGNMENT, GEOMETRY, SET THEORY

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE