〈 Berger | Dillon 〉

A straight line may be the shortest 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 between two points, but a "Brachistochrone" curve is the path of least timepic.twitter.com/aWPoz9X6i9

A "Cycloid" curve is one for which all objects take the 𝑠𝑎𝑚𝑒 amount of time to reach the bottom • If this seems counterintuitive, remember that 𝑚𝑔ℎ=½𝑚𝑣², and so objects starting higher will have a larger final velocitypic.twitter.com/EV4ZzT6YFo

We learn in high school that the "period of a pendulum is independent of its amplitude"--i.e that it's isochronus. • This isn't quite true; it's only true for *small* angles θ • In reality, a pendulum's period is only independent of its amplitude if it moves along a cycloidpic.twitter.com/d1Vh1VlJ9u