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Circular Sector Line Picking

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CircularSectorLinePicking

Pick two points at random in a circular sector of radius 1 and central angle theta, and consider the length s of the line joining them. The following table summarizes approximate values of the mean s^_ for various theta. The case theta=2pi corresponds to disk line picking.

thetas^__(approx.)s^__(exact)OEIS
1/2pi0.47387...(32)/(135pi^2)[6ln(2sqrt(2)-2)94sqrt(2)+48pi-3]A130204
pi0.70605...(64)/(135)(12pi-23)/(pi^2)A130203
2pi0.90541...(128)/(45pi)A093070

See also

Circular Sector, Disk Line Picking

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References

Sloane, N. J. A. Sequences A093070, A130203, and A130204 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Circular Sector Line Picking

Cite this as:

Weisstein, Eric W. "Circular Sector Line Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CircularSectorLinePicking.html

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