Isosceles Planar Subsets

A finite planar set is k -isosceles for k ≥ 3 if every k -point subset of the set contains a point equidistant from two others. There are three nonsimilar 3-isosceles sets with five points and one with six points. Eleven 4-isosceles sets with eight points are noted, and it is conjectured that no 4-isosceles set has nine points. Exactly one 4-isosceles 8-set has four points on a line, and every 4-isosceles set that includes the vertices of a square has fewer than eight points. <lsiheader> <onlinepub>26 June, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>19n3p391.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader>

Authors and Affiliations

1. AT\&T Labs—Research, Florham Park, NJ 07932, USA fish@research.att.com, , , , , , US

   P. Fishburn

Received February 1, 1997, and in revised form June 24, 1997.

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