Well, as a computer scientist, I'd hope you use pi * r * r, because there's no reason to compute tau/2 every time, and pow() is needlessly inefficient for integ

Well, as a computer scientist, I'd hope you use pi * r * r, because there's no reason to compute tau/2 every time, and pow() is needlessly inefficient for integer powers (on all languages I know. ~6 times slower in python). I'd expect you to make the same optimizations with the analogous equations, but that shouldn't have any bearing on which constant is better for learning, etc.