But why are there 2*pi radians in a circle, instead of defining it as pi?
EDIT: I meant redefining pi instead of the radian.
EDIT: I meant redefining pi instead of the radian.
Better yet, I think the unit of angle we should use is the 'full rotation' ('rot'?)
So instead of 360 degrees, or 2pi radians, we say 1 rot.
The many factors of 2pi in common equations imply we got this wrong.
> The second reason is that τ corresponds to one turn of a circle, and you may have noticed that “τ” and “turn” both start with a “t” sound.
e^(i * π) = -1, where i is the imaginary unit
would not in fact hold if we changed the definition of the radian. It's just the mathematically natural way of expressing arguments to trigonometric functions.
e^(2πi) = 1
e^jpi + 1 = 0
The reason for this form is that it doesn't just contain an imaginary unit and the two most popular constants but the additive and multiplicative identities.