Name: Pi O'clock
Rating: 4 (1 reviews)
Author: pi-oclock

Pi O'clock turns your watch into a unit circle.

Angles run counterclockwise from 0 at 3 o'clock (positive X axis), just like in trig class, and every hand is a vector:

• Second hand: an arrow whose tip rides the unit circle, with dotted projections onto the x and y axes, so you see cos θ and sin θ every second.
• Minute hand: a polar angle, with a dashed θm arc measured from 0. Below the x axis it sweeps the short way and reads −θm.
• Hour hand: lights up the quadrant it's in with a bold arc on the circle.

Ticks mark every π/6, π/4 and π/3, with callouts at each π/4.

The hands are offset so that at exactly 3:14:15 all three point at π. It's 12-hour time, so Pi O'clock happens twice a day, and you'll be awake for one of them. When it hits, the whole face flips to white and shows a giant π.

The second hand and projections hide in low-power mode to save battery. On AMOLED watches, always-on mode shows just the hour and minute hands as sparse, shifting dots to protect the screen.