[DavidSJ]

To address the problem they discuss at the end with defining Θ = e^2πi, they could instead define Θ(x) = e^2πix, the circular analog to the exponential function exp (which is really more fundamental than exp(1) = e anyways).

[abecedarius]

Note there's an existing notation which I've mostly seen in lower-class settings like high-school textbooks: r <angle-sign> theta, for the complex number r e^(i theta). Optionally leave out the r.

So you have that "most beautiful formula in all of mathematics":

<angle-sign> tau = 1

[DavidSJ]

> <angle-sign> tau = 1

Who knew that if you go around in a circle you get back where you started?

[dTal]

And here it is in Unicode glory:

∠τ = 1

[abecedarius]

Thanks, I should've figured there'd be a character.