03:14, the Pi minute
A constant that never resolves, pinned to a time that arrives twice a day.
The coincidence that made a holiday
Pi begins 3.14159, and in month-day notation the fourteenth of March reads 3/14. That coincidence produced Pi Day, marked in schools and physics departments since the late 1980s.
The clock offers the same coincidence twice a day. 03:14 is the digits of pi to two places, arriving in the small hours and again in the afternoon.
Why mathematicians like it more than the date
The date version depends on an American convention. Written day-first, the fourteenth of March is 14/3, which is not pi at all.
The clock version has no such problem. 03:14 reads the same everywhere the twenty-four hour clock is used, which makes it the more durable of the two references.
The minute after
Those who want a third decimal take 03:14 and then wait a minute, because 03:15 rounds correctly: pi to three places is 3.142, but the fifteenth minute is what the date convention gives you on 3/14/15.
The argument about which is more correct is older than the holiday and shows no sign of resolving, which is fitting.