Coding classes in Torfaen

Draw a line out from the centre of a spiral and measure how far each turn is from the middle. For an Archimedean spiral, like a rope coiled on a deck, each turn is a fixed distance further out, so the differences between measurements stay the same. For a logarithmic spiral, the shape many shells approximate, each turn is a fixed multiple of the last, so the ratios stay the same. The learner codes both tests in Python and asks which list varies less. The measurements below are invented for the lesson, not taken from the grotto.

To make the verdict fair, the program divides each list's spread by its average, so a list of ratios near 1.5 and a list of gaps near 4 millimetres can be compared. For the shell, the ratios vary by under 1 per cent while the gaps vary by more than 50. For the rope it is the other way round. The shell grows by about 1.51 times every turn, so it needs fewer than eight turns to grow from 4 millimetres to 100; the rope, adding 4 millimetres each time, needs 24.

Then the learner draws the shell spiral with a turtle, using the rule that radius equals a starting size times e raised to a growth rate times the angle. One more fact falls out: a logarithmic spiral cuts every line from its centre at the same angle, here about 86 degrees, which is why it looks the same at every size. And there is a trap. The formula needs the angle in radians. Feed it 360 for one turn instead of two pi, and the program says the spiral grows eighteen billion times in a single turn.

Asking for the numbers behind a neat story is a habit a Torfaen teenager can build by coding through 2026. The longer argument is in why teenagers should still learn to code in 2026.