Online coding and Python classes in Downpatrick

OpenStreetMap supplies 40 shops inside a rectangle over Downpatrick; where a shop is drawn as an outline, its centre stands in for it. Positions are converted to metres. Welzl's algorithm then builds the smallest enclosing circle: it takes the shops one at a time, and whenever a shop falls outside the current circle, it rebuilds the circle so that this shop sits on its edge. The final circle always rests on two or three points, its support points; every other shop could move a little without changing it.

Here the tightest circle rests on just two shops, the two farthest apart, and the brute-force search agrees at 1,834.3 m after 15,409 checks against Welzl's 229. The box-centre shortcut happens to come within 22 m, but the average-position shortcut needs a radius 504 m larger, because the average is pulled towards wherever shops cluster: the true centre is 509.4 m away from it. The second experiment uses all 5,865 building centres in the rectangle. With the buildings shuffled, the algorithm needed a median of about 50,200 checks over 20 shuffles. Fed them sorted from west to east, it needed 239,155, and sorted east to west, 205,503. Sorted input keeps putting the next point outside the circle, forcing rebuild after rebuild, which is why the algorithm shuffles first.

A Downpatrick teenager who can test an algorithm on its worst input will not be fooled by code that only works on tidy examples, and Python is where that habit is formed. The longer argument is in why teenagers should still learn to code in 2026.