Mysterious Spheres
This article and round puzzle are the first in a series by Chris Maslanka, puzzle master and author of The Guardian‘s Pyrgic Puzzles. Here he ‘sets the ball rolling’ with a conundrum concerning ancient stones….
The sphere has always been regarded as special, and it is natural that early cultures should seek to represent this 3-dimensional ideal in material form. The earliest durable material workable by Man was stone…
Stone spheres are found scattered at various sites around the world. Perhaps the most famous are those discovered in the 1930s by men of the United Fruit Co when they were clearing the jungle for a banana plantation along the Southern Coast of Costa Rica.
Unfortunately many of these bolas were dynamited as they were thought to contain hidden gold while others were looted to adorn gardens or parks, where many are to be seen to this day. Luckily not all of these artefacts of a lost civilisation were destroyed by modern civilised men. The largest collection conveniently gathered in one place may be viewed in the courtyard of the National Museum of Costa Rica in San José.
Most are made of granite and have diameters ranging from a few centimetres to over 2 metres and they weigh up to 16 tons. It is thought that they are the work of the Pre-Columbian Diquis culture about which little is known apart from the fact of their having existed.
Without a cultural context it is hard to be sure how these stone spheres were made to such a high degree of sphericity or how they were used, but it is clear that the shape had special significance. After all, the sphere is not only the most symmetrical of forms (it is similar to all other spheres, it looks the same from all angles and orientations, and all of its cross-sections are circles) but it also has the useful property that it may be rolled in any direction, which is no doubt how several of them ended up hilltops.
Of course what can be rolled up a hill may also run down. A memorable piece of modern product placement takes place in The Raiders of The Lost Ark in the opening sequence of which Indiana Jones has to escape from just such a rolling sphere.
Puzzle No. 1
Two spheres stand in contact on a flat and horizontal plane. The larger has a radius of 9 metres, the smaller a radius of 4 metres. How far apart are the points of contact with the ground?
Thruppence extra:
What if the radii were R and r— how could you work out the answer then?
Answers and next puzzle to appear…
A round puzzle by
Chris Maslanka
©CMM 2012
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