Consider the Frenet-Serret apparatus. We use tau to represent torsion. The Tau Manifesto proposes we replace it with N - that not only breaks the "scalars are lower-case Greek, vectors are capital Latin" pattern, but N is already used to represent the normal vector. And this is somewhere the circle constant (in whichever form) comes up frequently.
Some people say we should use e for the base of natural logarithms, but that's crazy. The letter e is already used for the charge on an electron, for the eccentricity of an ellipse, and for orthonormal basis vectors. Oh, and it's the identity element in group theory. Exponentials and logarithms show up in all those contexts, so the risk of confusion is too great. Using e also breaks the convention of using lower-case Greek letters for fundamental mathematical constants (such as the circle constant π, the golden ratio φ, the Euler–Mascheroni constant γ, and the Feigenbaum constants α and δ).
I'll keep using β = 0.367879..., thank you very much. Then the base of natural logarithms is 1/β, and 1/β^(iπ) = -1. How beautiful is that? Now, some people say that writing exponential growth as β^(-x) is confusing, but I say, come on, it's only a minus sign!
