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.

**References**

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

1999-05-25