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 think when someone uses infinity in a problem, all bets are off. If the balls are all equal in size, the proportion of gaps to balls will stay the same, so I can't see how the triangle can become "more" covered. If we could use different size balls there could be overlap as seen from above.<br><br>
Here's a kicker: "as seen from above", the balls are 3D, so viewed from different angles will give different answers.

Posted by bob909 on 2004-09-21 14:05:15