While browsing through the internets, I stumbled upon an essay that changed my life. This essay, The Tau Manifesto, has forever changed the way I think about the number π (pi). The number π≈3.14 seems to hold a very special place in popular culture and Mathematica alike. After all, it appears in the most intriguing places in mathematics--it is all over the place in geometry, physics, probability theory, the list goes on. People go through all the trouble to memorize pi to absurd precision to demonstrate memorization skills, people wear t-shirts emblazoned with that Greek letter, and people celebrate March 14 as "Pi Day." I am here to spread the word that we as a society are obsessed with the wrong number. We should instead be obsessed with 2π. Let me explain.

A circle is the set of all points a distance r from a given point. As we all know from elementary geometry, π is defined to equal the ratio of the circumference of a circle to its diameter, which is twice its radius r. I sincerely hope I am the not the only one here that finds the definition of π a bit odd, leads to the somewhat awkward identity C=2πr. That's right: the most fundamental relation between the "length" of a circle and its radius involves the number 2 multiplied by a constant. It is not only here where pi is found multiplied by a two, either. A full rotation is equivalent to 2π radians, meaning that the period of the sin and cosine functions is 2π. The formula for the Gaussian distribution is normalized by the square root of 2π. The nth roots of unity are given by the formula e^(2πi/n). Please read the article. Any doubts as to the fundamental-ness of 2π will be dispelled.

The author of this particular article, Michael Hartl suggests a new "circle constant" equal to 2π to be used instead. He denotes this constant τ (tau) for a variety of reasons, such as its aesthetic resemblance to the familiar π and its connotation as a full "turn". With your help, we can all put an end to this notational silliness. It can and should be done! As for myself, I have used the number τ for the past week, and I am not ever going back. (For the record, I am studying the wave and heat equations and Fourier series.)

Oh, I almost forgot! On Tau Day, June 28, feel free to treat yourself to a full τ radians of a pie (twice as much as you would get on March 14)! Thoughts?

Pi is right and always will be 2n isn't going to take over pi as pi is used better to find the circumference of a circle. I admit I didn't read all of it but pi is more widely used and 2n just won't become the "new pi" as few people know about it. 2n makes some sence but pi shows the relationship between a circles radius/diameter and circumference better then 2n . I don't care if you delete this post 2n will remain overshadowed by pi but I will when I'm not tired fully read the link and edit this to better suit my argument.

The purpose of this thread is precisely to get the word out that π might not be as fundamental a constant as we all were taught. Of course π as we all know it will still be around. One of the most convincing reasons for using τ alongside (if not instead of) π is to help trigonometry students get a better handle on radian measure of angles. In my experience, it is by the convention of naming angles as fractions or multiples of π (equivalent to one "half-turn") that many students get confused. Radian measure is the measure of arc length over the radius of a sector with that angle. For example, it is not intuitive that one fourth of a full rotation (equal to 90 degrees, a right angle) is π/2 radians. This can be avoided by speaking in terms of τ. Then, the angle of a quarter of a rotation becomes a simple τ/4. As for illustrating the circumference:diameter ratio, π is perfect. However, just how often do math students do calculations involving a diameter? Practically never. You almost never see the area formula for a circle written as (π/4)D^2, and even the surface area for a sphere written as πD^2. For whatever reason, a circle's diameter is really only used in the formula C=πD. Since the diameter is not the "standard" measurement of a circle, it follows that π is not the fundamental circle constant. All in all, whether or not it is the popular thing to do, using τ is a totally valid alternative to using π (to say the least).

T does seem like a viable option instead of n and I think that it will be used but not as much as pi as everyone has grown up with it and is use to that limitless number. Wow this makes me think about maths in a whole new level.