Tau (mathematical constant)

Tau () () is a mathematical constant that is the ratio of a circle's circumference to its radius. It starts as 6.283185307179586, and continues without end in a way that is not predictable. Numbers like this are called irrational numbers.

The radius is the shortest connection between the center and the circumference of a circle. The circumference is the distance around a circle. Even though the radius and circumference are different for different circles, the number tau remains constant: its value never changes. This is because the relationship between the circumference and radius is always the same.

Fundamentals
Definition
 is commonly defined as the ratio of a circle's circumference  to its radius :

Approximate value

Tau is often written as . It is also an irrational number, meaning it cannot be written as a fraction (), where 'a' and 'b' are integers (whole numbers). This basically means that the digits of tau that are to the right of the decimal go forever—without repeating in a pattern, and that it is impossible to write the exact value of tau as a number. Tau can only be approximated, or measured to a value that is close enough for practical purposes.

A value close to tau is 6.283185307179586476925287. Computers can be used to get better approximations of tau.

 Tau in real life 
There are different ways to calculate many digits of tau. This is of limited use though.

Tau can sometimes be used to work out the area or the circumference of any circle. To find the circumference of a circle, use the formula τ × r (Radius). To find the area of a circle, use the formula τ / 2 × r² (radius squared). This formula is sometimes written as , where A is the variable for the area.

People generally celebrate June 28 as Tau Day, because June 28 is also written as 6/28, which represents the first three numbers 6.28 in the approximation of tau.

 Tau in programming languages 

This table lists some programming languages that have Tau, the circle constant for converting between turns and radians. All of these programming languages use the name "Tau" in some casing, but Processing also has "TWO_PI" and Raku also has the symbol "τ" for the same value.

 Language  Identifiers  First Version  Year Released C# / .NET  System.Math.Tau and System.MathF.Tau  5.0  2020 Crystal  TAU  0.36.0  2021 Eiffel  math_constants.Tau  Curtiss  Not yet released GDScript  TAU  Godot 3.0  2018 Java  Math.TAU  19  2022 Nim  TAU  0.14.0  2016 Processing  TAU and TWO_PI  2.0  2013 Python  math.tau  3.6  2016 Raku  tau and τ     Rust  std::f64::consts::TAU  1.47.0  2020 Zig  std.math.tau  0.6.0  2019

Related pages
  π (mathematical constant)
 List of numbers
 Irrational numbers
 Square root of 2
 Golden ratio
 e (mathematical constant)
 Squaring the circle
 Transcendental number

 References 

Category:Geometry
Category:Irrational numbers
Category:Transcendental numbers
Category:Mathematical constants