Stonehenge, Wiltshire

The megalithic monument of Stonehenge, near Amesbury, about 6 miles north of Salisbury, has been credited with various mathematical properties, ranging from exhibiting the Theorem of Pythagoras to being a sophisticated astronomical observatory, though evidence is pretty scanty. Sadly, due to the number of people wanting to visit it, one can no longer get very close to it. One gets a good overall view driving on the A303 or the A360, but it is hard to appreciate the size of the stones except by a proper visit, though the current arrangements get you rather closer than the previous arrangements.

There is a legend that one cannot count the number of stones and get the same number twice. In a way this is not surprising as there are a number of smaller stones and it's not clear which ones should be counted. According to Aubrey, Charles II, fleeing after the Battle of Worcester in 1651, stayed in the neighbourhood for a few days and was unable to count the stones, though this may say more about Aubrey's reportage or about Charles' mathematical abilities or about Charles' state of mind than about the legend. [Child, pp.106 & 153-154.] This legend is associated with several other rings of stones, cf Aylesford and Bodmin. One version says that someone tried to count the stones with the assistance of a large basket of a known number of buns. She set a bun on each stone to show it had been accounted for and she intended to count the number left in the basket to determine the number of stones marked. However when she looked back, she saw the Devil eating all the buns. [Burton, pp.22-24]

There are some aspects of the structure which show some mathematical competence. The outer ring of big (sarsen) stones is basically circular with lintels which have mortise and tenon joints onto the uprights and tongue and groove joints from one lintel to the next. Further the lintels are curved to make the circle. The inner horseshoe of even larger stones has lintels which are joined to the uprights with mortise and tenon joints. The uprights of the horseshoe are somewhat tapered, possibly a perspective effect to make them look bigger, and the lintels are also tapered, possibly to make them appear straight up when viewed from the ground. These structures are dated to about 2300 BCE. It is believed these joints were cut after the uprights were in place and with a timber framework around the uprights, but it still seems to require a certain amount of geometric skill - one would not want to keep trying to see if the piece fits. The long avenue extending from the axis of the horseshoe does point to about the point of midsummer sunrise and is dated to about 3000 BCE.

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An extract from The Mathematical Gazetteer of the British Isles created by David Singmaster

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