Re:The Pi Manifesto
by ianterrell on Tuesday July 05, 2011 @02:58PM
(#2731084)
A quarter arc of the unit circle is a quarter τ (τ/4). A half arc of the unit circle is a half τ. A 5/19ths arc of the unit circle is 5/19ths τ.
How much simpler could it get?
Defining the unit circle as a circle with area τ is a contradictory statement and is semantically invalid.
A quarter arc of the unit circle is π/2. A quarter arc of the circle with area 2π, though... Here, let's do it in τ for fun. :3
So, the circle with area τ has radius sqrt(2) (from A = πr^2), diameter 2sqrt(2), and circumference τsqrt(2) (from C = Dπ), thus a quarter arc of that circle is τsqrt(2)/4. That's not a pretty number at all to work with.
Maybe keeping the unit circle at its current size is a better idea.