A geometry problem by Angela Richardson

Geometry Level pending

What is the mean distance between two points on the circumference of the unit circle? (tau=2pi)

1 \frac{8}{\tau} \frac{16\tau}{3} \frac{16}{3\tau}

Angela Richardson by Angela Richardson , 26, United Kingdom

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1 solution

Aaaaaa Bbbbbb
May 9, 2014

D(A, B), A, B are on the (0), denote: ∠ A O B = x , \angle{AOB}=x, It is easy to see that it gets the same result for x is of the range: [ 0 , π ] o r [ π , 2 π ] . [0,\pi] or [\pi,2\pi]. So the average D(A,B) is: e v e r a g e ( D ( A , B ) ) = 2 2 π ∫ 0 π 2 s i n ( x 2 ) d x = 8 2 π everage(D(A,B)) = \frac{2}{2\pi} \int_0^\pi 2sin(\frac{x}{2}) dx = \boxed{\frac{8}{2\pi}}

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