I have found the idea of tau useful even though I have never used it in writing.<p>One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. If these formulas are written in terms of tau, they may become slightly easier to memorize and manipulate. Perhaps so, but I don't really care about this. It’s not a big difference. Besides, there are also lots of formulas that are easier to memorize and manipulate using pi instead of tau. The probability density function of the standard Cauchy distribution f(x) = 1/pi * 1/(1 + x^2) is one example.<p>However, to get a deep understanding of mathematics, I want to understand the connections between different parts of mathematics. If I see a mathematical formula with the constant pi in it, I ask myself: "How is this connected to circles?" The idea of tau taught me that that 2pi is the natural state of affairs. If I see pi by itself, I need to ask myself: "How is this connected to half-circles? Or has the multiplier 2 been cancelled away?”<p>So, why does the pdf of the standard Cauchy distribution above contain pi instead of 2pi? What is the standard Cauchy distribution anyway? Take a gun that shoots particles in random directions, and place it one unit distance away from an infinitely long wall. Standard Cauchy distribution is where the particles will hit the wall. The particle will only hit the wall if it is shot in a direction towards it. This corresponds to 180 degrees - and there you have it: the connection to half-circles. Of course, you also have to work out the technical details. But on an intuitive level, when I see pi in the pdf of the standard Cauchy distribution I don’t think about how the missing multiplier makes it easier to remember a bunch of symbols; I think of particles hitting a wall.