Re: [math-fun] Asimov's correlation problem

Let e0, … , en be n+1 unit vectors giving the vertices of the regular simplex centered on the origin of R^n. e0+ … +en = 0 (1) Take the inner product of each side of (1) with itself: (n+1)1 + (n+1)n c = 0 (2) where c is the cosine of the angle formed by any two distinct vectors. Solve (2) for c: c = -1/n. -Veit

On Nov 5, 2015, at 3:46 PM, Dan Asimov <asimov@msri.org> wrote:

Question: ---------

Is there a more immediate way to see that this number is -1/n ???

—Dan