For points in the Plane, there are at least
different Distances. The minimum Distance can
occur only times, and the
Maximum Distance can occur times. Furthermore, no Distance can occur as often as
times. No set of points in the Plane can determine only Isosceles Triangles.
See also Distance
Honsberger, R. ``The Set of Distances Determined by Points in the Plane.'' Ch. 12 in Mathematical Gems II.
Washington, DC: Math. Assoc. Amer., pp. 111-135, 1976.
© 1996-9 Eric W. Weisstein