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?

Balls do not tesselate, due to there convex nature.

However, with the balls getting smaller all the time, will the gaps between disappear?

As far as the eye can see, you would probably say yes they do, but when using a microscope you would still see gaps,  so you would need more infinitely smaller balls.

You will at some point reach the atomic level, if you keep going on from this and look under an electron microscope, the only gaps will be between the atoms themselves, to the naked eye this would look for all intents and purposes to be a solid mass.

So to answer the question. YES and NO.

Posted by Juggler on 2004-09-17 12:18:26