Coding classes in Renfrewshire

The sizes are invented. The leaf is a straight span 20 metres long, lying flat across the channel when closed. For a fixed hinge, the tip simply swings around the pivot: at an angle a it sits at 20 cos a across and 20 sin a up. For a rolling lift, the land end carries a curved segment of radius 4 metres that rolls back along a flat track without slipping. No slipping has a precise meaning: when the segment has turned through an angle a, measured in radians, its centre has moved back by exactly 4 times a metres. The learner writes the tip's position as that backwards shift plus a rotation, two equations in the angle, which is what mathematicians call a parametric curve.

At small angles the two designs barely differ. As the leaf rises, the rolling version pulls back and climbs higher: at 70 degrees its tip is more than a metre further back from the channel and 2.6 metres higher than the hinged leaf's, so boats get more room. The price is that the whole leaf travels back almost 5 metres, and its tip covers 27.1 metres of path against 24.4 for the hinge. Plotting both paths shows the rolling tip tracing a stretched, cycloid-like curve rather than a circle.

Then the bug. Trigonometry functions in Python expect radians, but it is natural to type the angle in degrees. A learner who uses 70 in the rolling rule instead of 70 degrees converted to radians gets the centre moving back 280 metres instead of 4.89, and a bridge that slides away down the road. The fix is simple, but spotting it depends on checking that the answer is physically possible, which is the real lesson.

A teenager in Renfrewshire should still learn to code in 2026 so that an impossible answer looks impossible to them. The longer argument is in why teenagers should still learn to code in 2026.