Do the three hands on an analog clock (hours, minutes, seconds) ever divide the face of the clock into three equal segments, i.e. 120 degrees between each hand?

(In reply to Solution by Nick Hobson)

Re: "In other words, whenever the angle between the hour and minute hands is 120°, the second hand is parallel to the minute hand!"

Of the 22 times per half-day that the hour and minute hands make a 120-degree angle, only twice (4 o'clock and 8 o'clock) does the minute hand parallel (coincide when looked at in 2-D) with the minute hand.

For example at 21.8182 minutes past 12, the minute and hour hands are separated by 120 degrees, but the second hand is between the 9 and the 10 on the dial, closer to the latter, while the minute hand is slightly past the 4.

Posted by Charlie on 2004-07-05 16:24:03