Refer to Points On A Circle.

(A) Seven points are placed on the circumference of a circle such that the distance between any two of the points, measured along the circumference, is an integer.

What is the smallest radius of the circle, given that each of the distances is unique?

(B) Seven points are placed on the circumference of a circle such that the distance between any two of the points, measured as a straight line, is an integer.

Determine the smallest radius of the circle. What is the smallest radius of the circle, given that it is rational?

Note: In Part (B) each of the distances may or may not be unique.

In part A, if this were a line segment instead of a circle, the problem would be about Golomb Rulers.

http://mathworld.wolfram.com/GolombRuler.html

I suppose this half of the problem could be called the "Golomb Protractor" problem.

Posted by Brian Smith on 2010-07-14 12:14:55