Online coding and Python classes in Didsbury

The learner fetches the outlines of Didsbury East and Didsbury West from the ONS ward boundary service, in its generalised form, as lists of grid coordinates. The shoelace formula gives their areas exactly: 3,647,598 and 3,353,073 square metres for these simplified outlines, about 7.0 square kilometres together. That is the answer to aim at. The two wards sit inside a rectangle 3.808 km by 3.536 km and fill 52.0% of it. The estimate is simple: scatter points in the rectangle, find the share that fall inside either ward, multiply by the rectangle's area.

Random points come from Python's usual generator. Halton points come from a short function: write the point's number in base 2 and mirror the digits about the decimal point for one coordinate, do the same in base 3 for the other. Each experiment is repeated 200 times, with a different random seed or a different random shift of the Halton pattern.

With random points, a hundred times more darts buys about ten times less error: 5.79% at 100 points, 0.71% at 10,000. That square-root rule is the signature of random sampling. Halton points improve much faster, so the gap widens as the sample grows, from 1.5 times at 100 points to more than ten times at 100,000. Put another way, 1,000 Halton points (0.56%) beat 10,000 random ones (0.71%). The advantage comes from evenness, not luck, and it is largest for smooth, low-dimensional problems like this one; in problems with many dimensions it shrinks.

Knowing that a smarter scatter can beat a bigger one helps Didsbury teenagers question simulations an AI hands them, which is a good reason to learn Python in 2026. The longer argument is in why teenagers should still learn to code in 2026.