As you may know, I have been strongly intrigued by the tau movement. This movement is promoting the idea that we should not be using pi as the circle constant, but rather 2π, which has been renamed with the greek letter tau.
This movement was started by Bob Palais of University of Utah when he wrote the article Pi is Wrong which was published in the Mathematics Intelligencer. Physicist Michael Hartl proceeded to write The Tau Manifesto, and founded Tau Day on June 28th (instead of Pi Day on March 14th) as well as the website www.tauday.com. This gave dozens of reasons in geometry, trigonometry, physics, and statistics why tau is more practical and natural than pi. On a side note, I currently have the world record for tau memorization at 2012 digits, but that's nowhere near the world record for pi memorization at 67890 digits.
If you have some more time, The Tau Manifesto is a fascinating read. I'd also recommend watching this video done by Vi Hart for an overview of the tau movement.
You can also click here to see all of the blog posts I have done giving details on why tau is better than pi.
Just two days before writing this, I found that someone was inspired by Hartl's Tau Manifesto to write The Pi Manifesto, which presents an interesting rebuttal for tau. This wasn't recent news in mathematics, but it was definitely news for me!
I found that all of the reasons for either side can actually be debated. I think this is the first post where there is actually a debate over what is the right answer.
An argument for tau is that the radius is what a circle is measured by. Dictionary.com defines circle as a closed plane curve consisting of all points at a given distance from a point within it called the center. Clearly, the radius is the main measurement here.
Pi supporters would then argue that the radius can only be found by taking the diameter and dividing it by two. When looking at a circle on paper, it is impossible to pinpoint the center and find the measurement out to the end.
Yet, constructing the circle requires knowing the radius. If you were to use a compass, you must put the point where you want the center to be and trace a line with a constant distance around it. This is the true way to form a circle. For practical uses, you would need circles to see what restaurants were within ten miles or something. In this case, ten miles is the radius, and you are constructing a circle with this measurement.
This example requires the choice between constructing the circle easier or deconstructing the circle easier. The construction requires the radius, while a circle already given uses the diameter.
An argument for pi is that the area formula, which is one of pi's most common uses, is messed up by this change.
A = πr^2 –> A = 1/2τr^2
Yet, tau-ists argue that this is more natural. First, there are many other shapes that have 1/2 at the beginning of their area formula. Triangles, trapezoids, and n-sided polygons all use formulas with a 1/2 in it. Second, the area formula can be proven (I will in a future blog post), and this proof's last step is to multiply 2πr^2 and 1/2. It turns out to be more natural just to tack on the 1/2 rather than hiding the 2π with it.
This is again an argument where we need to choose between having a natural number or an efficient number. It is clear that tau is the constant that belongs, but we have an opportunity to simplify the equation.
Both manifestos list other reasons that take longer to explain, but are very interesting (I think a lot more interesting than the two above). These involve finding measurements of the unit circle, graphing trigonometric functions, and rewriting Euler's identity.
Because math is such a definitive discipline, it is rare for Cool Math Stuff posts to have comments. I strongly encourage you to comment on this post. After reading both manifestos, watching several YouTube videos, and seeing lots of press coverage, it is difficult to take a side. Comment what you think about the different arguments (I think the three I listed earlier are the closest arguments to call), and if you are a Tau-ist or not. This is one of the few chances where you can get into a debate about mathematics!