A pool rack is an equilateral triangle, filled with 15 equal-sized balls. Seen from above, we'd see a triangle, with 15 circles within.
Imagine we used smaller and smaller balls. The more the balls, more area of the triangle would be covered.
In the limit, with infinite balls, would all of the triangle be covered?
I believe that the triangle will never be covered. I believe there will always be space between the circles to ininity. I liken this to Archimedes attempts to determine Pi by using polygons to fill a circle. He kept getting closer and closer, but because there was always space between his polygon and the perimeter of the circle, it never reached the exact anwer. I suspect that the uncovered area will infinitely grow smaller, but never be completely covered.
PS>I see that Charlie has posted 3 times. I wouldn't be surprised if he has written a program that will show what the area uncovered is for poolballs = n.
Anyway, that's my story, and I'm sticking to it. Well, at least until someone shows me that I'm wrong. It won't be the first time, and it won't be the last.
My one and a half cents
