A new section of The Tau Manifesto: Getting to the bottom of pi

Happy Tau Day

It seems like these guys are fighting an uphill battle, not that I'd want to discourage it. It's simply much easier to visualize the path traced when you relate the radius to the circumference of a circle rather than its diameter, since there's only one point to focus on at a time as you rotate around the axis. Pi is insidious as it's only much later that this foundation begins to appear problematic.

[My analogy was not very good. The circumference is the only dimension of a circle stated in terms of diameter, not radius, and so substituting tau for pi is simply relating the radius of a circle to its circumference instead of its diameter. Circumference = tau * radius. This has the benefit of bringing the circumference formula in line with all the other circle equations.

When we look at the area of a circle, tau is not very intuitive, however. The formula for the area of a circle uses the square of the radius, so there's not an intuitive way to factor two into the equation without just making extra mental work for yourself.

For volume, the effect is somewhat neutral. Volume = 4/3 pi * radius^3 = 2/3 tau * r^3. 2/3 vs. 4/3 doesn't seem to add much insight into the equation.

Circumference = tau * r

Area = 1/2 tau * r^2

Volume = 2/3 tau * r^3

4th dimension circle = 3/4 tau * r^4? : P

Maybe there's something to this...]

Huh. Section 5.1 (one of the new ones) is presented as this new epiphany about hyperspheres and tau, but I made a post back in 2010 about this ( http://www.blahedo.org/blog/archives/001083.html ), emailed Hartl at the time, and he said he'd already thought of that. Still, cool to see that my observation was worth (eventually) including in the manifesto itself. (He did elaborate on the idea considerably, of course.) ;)

"pi is a lie" and "pi is wrong" are incredibly disingenuous slogans. I would be really excited about this site if it weren't for these sensationalist remarks at the top. It's sad, because their main content is all about mathematical reasoning, which overall they do a fine job presenting.

pi is not a lie. It's not part of some conspiracy theory among math elites to mislead the masses. It's not about math bureaucrats refusing to admit they were wrong. Everything they told you about pi is true (or it isn't, but in that case it's not true of tau either). pi and tau are really just two different notations for the same concept. Only perhaps one is more elegant and convenient than the other, making it more fundamental in some mystical way (and perhaps preferable if you ever need to convince visiting aliens that you are intelligent).

Am in and converted!