Ever wondered what the time would be when clock hands have a certain angle between them? Yes me too! All the time! After pondering the issue I posed it to my father, who came up with an elegant formula.
Given an hour (H) between 0 and 11 and and angle (A) between +/-360°, the minutes (M) before or past before the hour is given by:
M = (60 x H /11) + (12A/66)
Give it a try for some different input values here. You’ll see some interesting anomalies around 11 and 12 o’clock. Try the values 11, 10 and “after”. You might think the answer ought to be a few minutes to 11. But it’s actually just after 12. That’s because I defined “after” as after the minute hand passes the hour hand, and the latter doesn’t catch up to the former until 00:00.