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?

(In reply to A Point? by bob909)

The uncovered areas get infinitely small with infinitely many of them; the covered areas get infinitely small with infinitely many of them.  Any argument that it's completely covered could be applied the same way to say it's completely uncovered.

Posted by Charlie on 2004-09-20 16:46:43