[orangecat]

Interesting. It's probably not worth defining a new constant for exp(2π), but this is a further demonstration of the Tau Manifesto's argument that 2π is much more of a fundamental value than π.

[garbagecoder]

Fundamental sounds like a value judgment. Pi is transcendental. 2 isn't. That's really the distinction. Unless there were other finite factors in pi, that is the number that's always going to have to be approximated in computation.

[ohwellhere]

"Tau is transcendental. 0.5 isn't."

It's definitely a value judgment. But the value judgment is: Is the radius or the diameter more fundamental to a circle?

[BlueTemplar]

As the Tau manifesto points out, tau/4 = pi/2 = lambda is pretty fundamental too ! (The "orthogonality constant" ?)

[garbagecoder]

Geometry isn't the only application of pi. Nor is the geometric interpretation the only way to determine what is "fundamental."

Why not use Darians? http://proper-pi-manifesto.com

[bmacho]

Fundamental sounds meaningless to me.

Talking about statements and words with meaning I am sure, that Tau is the more useful circle constant out of these two: less symbols, conceptually clearer equations.

Also turn is generally a more useful measurement unit for angle than radian or degree, but radian has its own merits, and not disposable, unlike pi.