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Oh, balls A record-breaking 34-ball, 12-storey tower with three balls per layer (photo a); a 21-ball six-storey tower with four balls per layer (photo b); an 11-ball, three-storey tower with five balls per layers (photo c); and why a tower with six balls per layer would be impossible as the “locker” ball just sits in the middle (photo d). (Courtesy: Andria Rogava)
A few years ago, I wrote in Physics World about various bizarre structures I’d built from tennis balls, the most peculiar of which I termed “tennis-ball towers”. They consisted of a series of three-ball layers topped by a single ball (“the locker”) that keeps the whole tower intact. Each tower had (3n + 1) balls, where n is the number of triangular layers. The tallest tower I made was a seven-storey, 19-ball structure (n = 6). Shortly afterwards, I made an even bigger, nine-storey, 25-ball structure (n = 8).
Now, in the latest exciting development, I have built a new, record-breaking tower with 34 balls (n = 11), in which all 30 balls from the second to the eleventh layer are kept in equilibrium by the locker on the top (see photo a). The three balls in the bottom layer aren’t influenced by the locker as they stay in place by virtue of being on the horizontal surface of a table.
I tried going even higher but failed to build a structure that would stay intact without supporting “scaffolds”. Now in case you think I’ve just glued the balls together, watch the video below to see how the incredible 34-ball structure collapses spontaneously, probably due to a slight vibration as I walked around the table.
Even more unexpectedly, I have been able to make tennis-ball towers consisting of layers of four balls (4n + 1) and five balls too (5n + 1). Their equilibria are more delicate and, in the case of four-ball structures, so far I have only managed to build (photo b) a 21-ball, six-storey tower (n = 5). You can also see the tower in the video below.
The (5n + 1) towers are even trickier to make and (photo c) I have only got up to a three-storey structure with 11 balls (n = 2): two lots of five balls with a sixth single ball on top. In case you’re wondering, towers with six balls in each layer are physically impossible to build because they form a regular hexagon. You can’t just use another ball as a locker because it would simply sit between the other six (photo d).
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