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Analog Clock Trivia?

Alright... now I've seen some pretty weird stuff on the Internet... but how about this?

Picture an analog clock with an hour hand, minute hand, and second hand, ticking every second.  Have you ever wondered...
  • How often is the second hand between the hour and minute hands?
  • At what time is the clock equally divided into three parts (by the positions of the hour, minute, and second hands)?
... ya, I think about this stuff all the time. (sarcastic)

Well... in case you were wondering, I've found the answers.  The second hand is between the hour and minute hands about 32% (13832 of 43200) of the time.  There are a total of 43200 possible positions for the hour, minute, and second hands on an analog clock.  That is, 60*60*12.

And... a perfect analog clock really never is divided equally into three parts by the hands (unless you count the times when the second hand is in motion to its next position... that is, in the middle of a "tick").  However, it is closest to three equal parts at 8:22:02 (either AM or PM).  At this time, the hour hand will be about 251.0166 degrees from 12:00:00 (moving clockwise, of course).  The minute hand will be at exactly 132.2 degrees from 12:00:00, and the second hand will be at exactly 12 degrees from 12:00:00.

Good to know, right?  It was so ridiculous, that I had to post it.  My apologies for completely wasting your time.

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