After watching the excellent piece of exposition on mathematical exploration by 3Blue1Brown guest Ben Syversen: “What was Euclid really doing?”, I discovered the fantastic web and mobile game Euclidea.

Geometry was never my favourite branch of mathematics, I always felt more drawn to algebra and more symbolic and abstract forms of reasoning. But Euclidea really does a masterful job of capturing the joy of exploration and problem solving through the lens of scaffolded puzzles of compass-and-straightedge geometric constructions.

As you construct each solution, they get encapsulated and added to your toolkit of re-usable constructions. It’s a best way to demonstrate the power of axiomatisation and iteratively increasing the levels of abstraction.