Coding classes in Carmarthenshire

The span comes from the record: about 25 metres, so the half-span is 12.5. The rise is not given, so the learner tries invented values, mainly 7 metres. The arch is modelled as half an ellipse. The learner then measures its length five ways: two quick guesses, two formulas found by the Indian mathematician Srinivasa Ramanujan, a curve made of many short straight pieces, and an exact method based on Gauss's arithmetic-geometric mean, which repeatedly averages two numbers in two different ways until they agree.

The quick guesses are a couple of per cent out either way, which on a real arch would be about 60 centimetres. Chopping the curve into straight pieces works, but slowly: every time the number of pieces goes up four times, the error drops about sixteen times, so 1,024 pieces are needed for sub-millimetre accuracy. Ramanujan's formulas, published over a century ago, are astonishing; the second is right to a few billionths of a metre here. The arithmetic-geometric mean reaches the exact value in only five rounds of averaging, because its error roughly squares away at every step.

Our own first version of the exact method had a bug and returned half the right length. It was caught by an easy test: when the rise equals the half-span, the arch is a semicircle, and every correct method must give pi times 12.5, 39.27 metres. Testing code against a case you already know the answer to is one of the most useful habits in programming.

Proving how accurate an answer is, rather than taking it on trust, is a skill Carmarthenshire teenagers gain by learning to code in 2026. The longer argument is in why teenagers should still learn to code in 2026.