Hello, its March 14 and its time for your annual reminder that π is wrong! Now that we usually construct circles instead of measuring them, its almost universal for the dimensioned parameter of a circle to be its radius rather than its diameter. This factor of two usually winds up attached to the dimensionless circle constant, π: the period of the sinus functions is 2π, the prefactor in Fourier transformation is 1/2π, the Planck constant is typically reduced to h/2π, and on and on. Its quite frequently easier to think in terms of τ = 2π ~= 6.3, the number of radians in one turn. There are many more examples than the ones Ive given above, some first elaborated by Bob Palais math.utah.edu/~palais/pi.html, others by Michael Hartl tauday/tau-manifesto. I will confess that the simplification which drove me over to the τ side is one of the most basic: before learning that π is wrong, I could never remember, without pausing to think, how many radians there are in a quarter-turn, where the sine vanishes. (Its τ/4.) If you are a person who frequently finds yourself writing down expressions containing π, have a look at the τ manifesto (feel free to groan and wish it wasnt called a manifesto). Try sticking τs in your own notes, maybe even in your presentations, and sneaking phrases like half-turn into conversations with colleagues and students. See how it feels. If you like it, let me know on 6/28.
Posted on: Fri, 14 Mar 2014 19:18:01 +0000
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