That's pretty amazing you came up with that in 9th grade. You may know this already but for anyone who doesn't, this is a result of covariance being an inner product [0]. Remember that the inner product of a vector with itself is the length of that vector squared. So if you had another data set, y1, ..., yN, the correlation ( = covariance / (std.dev(X)*std.dev(Y)) ) is the inner product divided by each length which, if you remember, is the angle between your vectors (datasets after removing the means.)

http://en.wikipedia.org/wiki/Covariance#Relationship_to_inne...