Re: [math-fun] n-dimensional geometry puzzle

Sorry if I'm being dense, but I don't see how Dan got On Fri, Jul 6, 2018 at 4:57 PM, Dan Asimov <dasimov@earthlink.net> wrote:

Here's my solution to the "n-dimensional geometry puzzle" below:

The center of the smallest sphere containing (1,0,...,0), ..., (0,...,0,1) in R^n must be at their centroid, which is

C = (1/n, ..., 1/n).

The distance from the point C to any of the basis vectors is sqrt(1-1/n).

I get sqrt((1-1/n)^2 + (0-1/n)^2 + ... + (0-1/n)^2) = sqrt((n-1)^2/n^2 + n(1/n)^2) = sqrt((n-1)^2+n)/n^2) = sqrt(n^2-n+1)/n, not sqrt(1-1/n). Am I suffering from end-of-workweek brain-fog? Jim