For a finite set of points in the plane the lower bound on the computational complexity of finding the convex hull represented as a convex polygon is easily shown to be the same as for sorting using the following reduction. For the set x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} numbers to sort consider the set ( x 1 , x 1 2 ) , … , ( x n , x n 2 ) {\displaystyle (x_{1},x_{1}^{2}),\dots ,(x_{n},x_{n}^{2})} of points in the plane. Since they lie on a parabola, which is a convex curve it is easy to see that the vertices of the convex hull, when traversed along the boundary, produce the sorted order of the numbers x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} .