by **metric man** » Sat Dec 24, 2011 12:34 am

Hi everyone,

I would like to say two things: First, that I agree with Spiked Math that areas of sectors provide an argument for [tex]\tau[/tex].

But I would even go beyond what Spiked Math said when writing: "I know in the Pi Manifesto it is stressed that when looking at areas it is a clear win for [tex]\pi[/tex]."

In my opinion, "tauists" are being too generous with our adversaries when they make such a concession regarding the area of a circle. I believe that when advocates for [tex]\pi[/tex] make such a claim, then advocates for [tex]\tau[/tex] are letting off the pro-[tex]\pi[/tex] people too easily.

First, let me say that I recently saw someone else make essentially the same argument that I am about to make, albeit with different words. I wish that I could give proper attribution, but I cannot remember where I saw the argument -- perhaps it was in this very forum.

In any event, pro-[tex]\pi[/tex] advocates will point out that the following formula looks so tidy:

[tex]\pi = \frac{A}{{{r^2}}}[/tex]

So it does. But in writing that formula, those who advocate [tex]\p[/tex] fail to have the courage of their convictions. They claim that diameter is the fundamental circle constant, not the radius. When it suits them, however, as it does here in order to make a succinct formula, then they are quick to abandon diameter and utilize radius in its place.

I say that the advocates of [tex]\p[/tex] do not have the right to refer to radius in the context of explaining any of the parameters of a circle. To be consistent with their own argument, they are logically bound to always refer to diameter and never to radius when discussing circles. And hence, the formula they should use is the much more cluttered version of the circle's diameter, as such:

[tex]\pi = \frac{4A}{{{d^2}}}[/tex]

In short, if pro-[tex]\pi[/tex] people don't like radius, if they don't recognize radius to be the fundamental circle constant, then they shouldn't use it.

Thanks to all of you who read my commentary.