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?

Tessellate: To cover a plane with identically shaped pieces which do no overlap or leave spaces. <br><br>

By definition, circles do not tessellate, so the obvious answer is NO.  If you have a near infinite number of balls, you also have a near infinite number of gaps.<br><br>

If you want to go down to the atomic level, even indiviual atoms are mostly space. So, if you had your "atomic glasses" on, the rack would appear to be mostly uncovered.

Posted by bob909 on 2004-09-17 14:28:27