Editing Convex hull (section)

===Brownian motion===
The curve generated by [[Brownian motion]] in the plane, at any fixed time, has probability 1 of having a convex hull whose boundary forms a [[Differentiable curve|continuously differentiable curve]]. However, for any angle <math>\theta</math> in the range <math>\pi/2<\theta<\pi</math>, there will be times during the Brownian motion where the moving particle touches the boundary of the convex hull at a point of angle <math>\theta</math>. The [[Hausdorff dimension]] of this set of exceptional times is (with high probability) <math>1-\pi/2\theta</math>.{{sfnp|Cranston|Hsu|March|1989}}