perplexus.info :: Just Math : A clock area

A clock area (Posted on 2023-08-23)

A clock has an hour, minute, and second hand, all of length 1. Let T be the triangle formed by the ends of these hands. A time of day is chosen uniformly at random. What is the expected value of the area of T?

No Solution Yet Submitted by Danish Ahmed Khan

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re(2): Computer method - faulty premise

| Comment 3 of 6 |

(In reply to re: Computer method - faulty premise by Brian Smith)

Aha! Good point.

Yes, the movement of the hands is not random; the 3 points are not independent. I did wonder about that, and I was going to comment that my premise might be wrong (or words to that effect); but I went ahead thinking that over the course of 12 hours it would average out.

It will be interesting to see how different the correct answer is.

Posted by Larry on 2023-08-23 13:17:39

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