Condition for Valid Time Indication/Corollary

Theorem

Consider an analogue clock $C$ with an hour hand $H$ and a minute hand $M$.

Let $\theta \degrees$ be the angle made by the minute hand with respect to twelve o'clock.

Let $\rho \degrees$ be the angle made by the hour hand with respect to the hour just past.

Then $C$ displays a valid time indication if and only if:

$\rho = \dfrac \theta {12}$

Proof

Follows directly.

$\blacksquare$