[Andria Rogava] As a physicist and keen tennis player, I would like to share an amusing “discovery” I recently made. In my office, I have about 20 used tennis balls and so decided to try building some tennis-ball “pyramids”.
As you might expect, a four-level pyramid has a triangular cross-section, with 10 balls at the bottom, followed by six in the next layer, then three and finally one ball on top (image top right). When I carefully removed the three corner balls from the bottom layer plus the upper-most ball, I ended up a with a beautiful, symmetric structure of 16 balls with three hexagonal and three triangular sides (image top left).
Interestingly, the corner balls in the second-bottom layer are kept in equilibrium, hanging over the layer below. These “exposed” balls are held in place because the balls directly above press down on them and into the two adjacent balls of the bottom layer – producing a pair of reaction forces to balance their weight. The torques are balanced too, with enough friction between the felt-covered balls to guarantee equilibrium.