11 Jul '06 21:081 edit

I just intend this puzzle as exploratory. I believe there's an answer, but I'm not sure.

Given a sphere radius x, draw a circle on it with a diameter d and circumference c. This circle has two center points, one closer to the circle, and one farther from it. Thus, it has two diameters, one to the closer center, and one to the farther one. Is an equation relating the two ratios of c/d to a constant?

If you use the closest point, then your ratio is between 2 and pi. If you use the farther one, then your ratio is between 0 and 2.

Given a sphere radius x, draw a circle on it with a diameter d and circumference c. This circle has two center points, one closer to the circle, and one farther from it. Thus, it has two diameters, one to the closer center, and one to the farther one. Is an equation relating the two ratios of c/d to a constant?

If you use the closest point, then your ratio is between 2 and pi. If you use the farther one, then your ratio is between 0 and 2.