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?

No. It is possible for any two hands to give a 120-degree angle, but not three. Consider, for example, the times of 4:00 and 8:00. The hour and minute hands give you a 120-degree angle, but the minute hand is on top of the second hand.

I'm working on proving the rest of it.

Posted by Eric on 2004-07-05 11:06:46