5 ms·
When you ask hard-core Tauists what the area of a unit circle is, do they actually answer "tau over two"? Or do they just say "pi"? By the way, this whole dis
by fexl 15y ago
When you ask hard-core Tauists what the area of a unit circle is, do they actually answer "tau over two"? Or do they just say "pi"?
By the way, this whole discussion reminds me of what W.V.O. Quine called "mathematosis".
- yobbobandana 15y agopersonally, i'd answer "half tau". half tau r^2 is a fine equation for an area.
- fexl 15y ago:) Still, two syllables instead of one. I suppose if I found myself writing "2 * pi" or "4 * pi^2" a lot, I might throw in a dash of tau here and there for brevity. Otherwise it's all the same to me.
- fexl 15y agoThough in fairness to tau, one can always choose a pithy question whose answer is shorter either way, to wit: What is the area of a unit circle? Pi. How many radians are in a circle? Tau.
- orangecat 15y agoAs the tau manifesto discusses, "half tau" is the more meaningful answer: the area of a circle is equal to the area of a triangle whose base is the circumference and whose height is the radius.
- lotharbot 15y agoIt's the integral of tau * r * dr from 0 to 1, which is tau/2.
- bascule 15y agoIt's τ/2. The area of a circle is τr²/2. You may be familiar with the idea of x²/2 from calculus: it's an integral, which can be used to compute areas.
- fexl 15y agoYes, that certainly is the integral of x * dx. So voila, there's your 1/2. And tau relates the triangle to the circle. Nice trick. Mind you, I don't have a dog in this hunt so I'm not all up to speed on it. All I know for sure is that tau = 2 * pi, so I won't be terribly upset if I see either usage. I generally favor the use of notations which better reveal an underlying concept, but I don't like it when people get all high and mighty about things.