The source of the conflict that oppose PI and TAU

An enlightening discussion about pi and tau.

The source of the conflict that oppose PI and TAU

by Apostoli » Sat Oct 25, 2014 6:31 pm

Hello,

All the problem betwen PI and TAU is comming of a bad definition of the notion of radian.
An angle is define like the SURFACE betwen too crossings lines, and NOT like an arc of circle.
So, if that, 360 degrees is equivalent to PI (PI*r2 , with r=1) and not to 2*PI.
With this definition of radian, we have the perfect eiPI=1 instead of eiPI=-1.
When I was yonger I have never liked this -1 but I didn't understood why.

That is the reason. A bad definition of the Radian.
Apostoli
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Re: The source of the conflict that oppose PI and TAU

by 1=0 » Sun Mar 19, 2017 11:26 am

There's good reason to define the radian as arc length/radius rather than sector area/radius squared, even if you don't count the fact that arclength is 1 dimensional and thus the most fundamental measurement or the factor of 1/2 in sector area coming from triangles.

Many things in trigonometry only work with radians and not any other system of measurement. With radians, cosine is the derivative of sine.
The Taylor series for all the trig functions and Euler's formula only work in radians. These things wouldn't work with areans. So changing radians won't work. If could just use any unit we wanted, we would probably just use rotations, but unfortunately, there are certain things that radians are needed jnstead of rotations. (Luckily, though, we have a convenient conversion factor between rotations and radians called tau).
τ>π
1=0
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