ncm writes in favour of τ against π: It's silly to memorize an absurd number of digits of pi and then be obliged to double them before they are useful.
I've no issue with having both constants about, using π or τ whichever is simplest, but I find that π feels more fundamental to me. A couple of considerations:
- The area of the unit circle is π. This seems as close to fundamental a fact of trigonometry as you can get. Perhaps trigonometry differs from folk geometry in finding the radius of a circle more fundamental than the diameter?
- Quite a lot of the Tau Manifesto is devoted to how much nicer things are if we express radians as lying between [0,τ] rather than [0,2π]. Well, radians are an equivalence class over all the whole continuum, and choosing to express radians over a positive interval to me strikes of failing to appreciate the symmetry of geometry. I find [-π,+π] more natural than [-τ/2,+τ/2], and I like having π being the opposite angle to 0. I do, I confess, view expressing right angles as τ/4 rather than π/2 more intuitive, since right angles "quarter" the plane.
I'm quite happy for people to prefer working with τ rather than π, but I would be unhappy with a calculator than had a τ key and no π key.