Philosophy of Mathspeaking topic

Roll a circle along a line, and a point on its rim traces not a straight path but a curved arch. The fastest way to slide down between two points is not the straight line but this arch flipped upside down. Why is the quickest path not the straightest one?

the brachistochrone, the cycloid

practice with this topic

Set the timer (5-30 min), take 20 seconds of prep if you like, start talking. Jot your thoughts onto the sticky-note board.