I placed six points on the circumference of a circle such that the distance between any two of the points is an integer. What is the smallest such circle I could use?
What if each distance must be unique?
When the sides are allowed to be nondistinct, there is a solution with radius 7/sqrt(3) = 4.01415...
the hexagon has side lengths 3,5,3,5,3,5, and diagonals of length 7 and 8. Labelling the vertices AF, the distances are as follows:
AB,CD,EF: 3
BC,DE,FA: 5
AC,BD,CE,DF,EA,FB: 7
AD,BE,CF: 8
working on the distinct sides version. initial results suggest the radius > 500. For a quadrilateral with distinct chord lengths, the smallest radius is 12.8102523...., and for a pentagon the smallest radius is 39.2938971....

Posted by sundberg
on 20040819 01:29:47 