Scientific American makes the case for replacing Pi with Tau, a constant equal to 2π:
The crux of the argument is that pi is a ratio comparing a circle’s circumference with its diameter, which is not a quantity mathematicians generally care about. In fact, almost every mathematical equation about circles is written in terms of r for radius. Tau is precisely the number that connects a circumference to that quantity.
But usage of pi extends far beyond the geometry of circles. Critical mathematical applications such as Fourier transforms, Riemann zeta functions, Gaussian distributions, roots of unity, integrating over polar coordinates and pretty much anything involving trigonometry employs pi. And throughout these diverse mathematical areas the constant π is preceded by the number 2 more often than not. Tauists (yes, they call themselves tauists) have compiled exhaustively long lists of equations—both common and esoteric, in both mathematics and physics—with 2π holding a central place. If 2π is the perennial theme, the almost magically recurring number across myriad branches of mathematics, shouldn’t that be the fundamental constant we name and celebrate?