Tau.jl

This Julia package defines the Tau constant and related functions.

tau ≈ 2*pi

Usage

After installing this package with Pkg.add("Tau"), it can be used as follows:

julia> using Tau

julia> tau === τ ≈ 2*pi
true

julia> typeof(tau)
Irrational{:twoπ}

Note: to input the τ character, type \tau then press Tab.

The tau variants of sinpi, cospi, sincospi, cispi, and mod2pi are also defined:

julia> sintau(1//4)
1.0

julia> costau(1//2)
-1.0

julia> sincostau(1//2)
(0.0, -1.0)

julia> cistau(1//2)
-1.0 + 0.0im

julia> modtau(9*pi/4)
0.7853981633974481

Alternatively, one can use the Unicode aliases sinτ, cosτ, sincosτ, cisτ, and modτ.

The tau != 2pi inequality

When this package was first created, the equality tau == 2pi did hold true, in accordance to the mathematical definition of the constant. However, that is not valid anymore -- the two values are only approximately equal: tau ≈ 2*pi.

For a detailed explanation of the reasons for this, see this document.