MathDB

An accurate 12-hour analog clock has an hour hand, a minute hand, and a second hand that are aligned at 12:00 o’clock and make one revolution in 12 hours, 1 hour, and 1 minute, respectively. It is well known, and not difficult to prove, that there is no time when the three hands are equally spaced around the clock, with each separating angle

\frac{2 \cdot \pi}{3}.

Let

f(t), g(t), h(t)

be the respective absolute deviations of the separating angles from \frac{2 \cdot \pi}{3} at

t

hours after 12:00 o’clock. What is the minimum value of

max\{f(t), g(t), h(t)\}?

Problem Statement