Whoa. I didn't have this geometric point of view down so I didn't understand at first what you meant, but now that I've thought about it for a few minutes it makes sense.

The prevalent intuitive meaning of correlation coefficient (at least the one I learned in the watered-down statistics-for-physics-students class) is "a measure of how well two variables correlate. 1 is well, 0 is not at all, -1 is backwards correlation." Hence, the first thing I thought of was that image. Many people who need to use this coefficient won't have taken linear algebra and it'll be a complication for them to learn that it's "the inner product of two random variablesies, so 0 means lots of correlation, pi means the opposite direction, and pi/2 means no correlation." Or maybe you use degrees, idk.

I like it, thanks for making this thread :D