3 ms·
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
by DavidSJ 3y ago
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 3y agoNote 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 3y ago> <angle-sign> tau = 1 Who knew that if you go around in a circle you get back where you started?
- dTal 3y agoAnd here it is in Unicode glory: ∠τ = 1
- abecedarius 3y agoThanks, I should've figured there'd be a character.