Abstract
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. 26 June, 1998 Editors-in-Chief: la href=../edboard.html#chiefslJacob E. Goodman, Richard Pollackl/al 19n3p391.pdf yes no no yes
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