simplex point picking

Given a simplex of unit content in Euclidean d-space, pick n>=d + 1 points uniformly and independently at random, and denote the expected content of their convex hull by V(d, n). Exact values are known only for d = 1 and 2. V(1, n) | = | 1 - 2/(n + 1) | = | (n - 1)/(n + 1), (Buchta 1984, 1986), giving the first few values 0, 1/3, 1/2, 3/5, 2/3, 5/7, ... (OEIS A026741 and A026741).

disk triangle picking | simplex | tetrahedron tetrahedron picking