Re: [math-fun] Puzzle: Find limiting angle as dimension -> oo

Let v_n be the vector in R^(n-1) defined as (1/n, 2/n,...,(n-1)/n).

Let w_n be the vector in R^(n-1) with the same coordinates in reverse order.

Find the limit as n -> oo of the angle between v_n and w_n.

A partridge in a pear tree?

(Try this without using numerical approximation or summation-of-powers formulae.)

Is there a simple geometric reason for the answer? I don't know.

--Dan

-- Mike Stay staym@datawest.net