Coding classes in Falkirk

The model is a famous one from botany, usually credited to Helmut Vogel. Seed number n is placed at an angle of n times some fixed turn, at a distance from the centre equal to the square root of n. Each new seed turns by the same amount from the last and sits a little further out. The only choice is the turn. The learner writes it in about ten lines of Python, draws a thousand seeds, then measures how close each seed is to its nearest neighbours.

Any turn that is a simple fraction of a circle fails. Two fifths of a turn means every fifth seed lands on the same line, so seeds pile along five spokes with empty wedges between them. A turn of 140 degrees is seven eighteenths of a circle and makes 18 spokes. The winner is the golden angle, 360 divided by the square of the golden ratio, about 137.5078 degrees. The golden ratio is the number hardest to approximate by fractions, so no seed ever lines up exactly behind an earlier one, and the nearest gaps are the largest and most even of all: they vary by just 1.7 per cent. Move the angle by half a degree to 137.0 and the variation nearly quadruples to 6.4 per cent.

Then comes the surprise. For every seed the learner records how many places back in the sequence its two nearest neighbours are. With the golden angle those gaps are always Fibonacci numbers, 1, 2, 3, 5, 8, 13, 21 and so on, each the sum of the two before. Near the centre the neighbours are 13 and 21 steps apart; further out 21 and 34, then 34 and 55, and at the rim 55 and 89. Those are the spirals the eye picks out, winding both ways. At 138 degrees the gap becomes 60, which is not a Fibonacci number, and the pattern loses its balance.

For a Falkirk teenager, then, learning to code in 2026 is how you catch the one wrong constant that an AI slipped in. The longer argument is in why teenagers should still learn to code in 2026.