You are provided with a circle, a triangle, and a square which each have the same length perimeter. If the circle is rotated, without slipping, around each of the other two, in which case will it rotate through the greatest number of degrees?

In each case, the circle will rotate through 360 degrees, PLUS the sum of the turns it makes.  The first 360 is because the perimeter is the same.  Each turn is the complement of the angle of the n-gon.

For the triangle, there are 3 turns of 120 degrees each, so the circle rotates through 720 degrees.

For the square, there are 4 turns of 90 degrees each, so the circle rotates through 720 degrees.

So, to me, it looks like they are the same (assuming it completes the final turn when it gets back to the starting point).

Posted by Larry on 2005-07-02 03:54:51