# 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.