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?

Given the point (1,0); (cos a, sin a) ; (cos b, sin b)

The determinantal formula for the area A gives:
2*A = sin a - sin b + cos a*sin b - sin a*cos b

This is from https://people.missouristate.edu/lesreid/AdvSol09.html?

Which confirms the 3/(2pi) solution with a tidy double integral.

I'm working on adapting that solution to this clock-bound variation.

Posted by Jer on 2023-08-27 10:23:45