Calculating distance in n dimensions

Question

Does this method work up to any spacial dimension? (5d, 10d etc)

http://freespace.virgin.net/hugo.elias/routines/r_dist.htm

p.s. If I'm getting this all fundamentally wrong somehow, please say.

Answer 1

Essentially yes. What you are looking at is euclidean distance; for instance take two vectors $\hat{j}$ and $\hat{k}$ you would take $||\hat{j}-\hat{k}||$ = $\sqrt{(j_1-k_1)^2+(j_2-k_2)^2}$

This works in nth dimension euclidean space $\sqrt{(j_1-k_1)^2+(j_2-k_2)^2+ ... + (j_n-k_n)^2}$