# Tau – A Mathematical Constant

**What is Tau?**

The constant is numerically equal to** 2*pi (2 times pi)**, and with value approximately** 6.28**. The ratio equates to 2*C/D. Where C is circumference and D is diameter of circle.**Applications of Tau **

- There are
**many expressions**that actually require**“2*pi” calculation**, having tau being equal to that simplifies them to great extent, for e.g**Circumference of circle = 2*pi*r = tau*r**. - Concept of tau can be useful in
**angular measurements**like angles in radians, representing as a complete “one-turn” and cos,sine functions in trigonometry have period of tau. - These concepts can be useful for
**teaching geometry**as would reduce the confusion of using “pi” and “2*pi” at many applications and would help get rid of factor of 2. - Tau
**simplifies euler’s identity**by eradicating the factor of 2. - It is
**useful at many places where “2*pi” are used**such as fourier transforms, cauchy integral formula’s etc.

**Criticism against Tau**

- Since it
**contradicts with the symbols of torque, shear stress and time**, this symbol has been a lot of criticism. - We already had a ratio of “C/D” equal to pi, having another circle ratio with factor of two will create confusion in choice.
- There exist
**formulas which look more elegant as expression of “pi”**rather than tau, for example, area of circle = pi*r*r = (tau*r*r)/2, introducing an extra factor of “1/2”.

**Coding Prospects**

Since Programming has always been trying to match up with mathematical advancements, symbol of tau has been introduced as a constant in recent python 3.6 under the math module. Below is the illustration of it.

## C++

`#include <iostream>` `#include <cmath>` `int` `main()` `{` ` ` `// C++ has no inbuilt tau but has inbuilt pi in cmath library` ` ` `// std::cout << M_PI; // this prints the value of pi` ` ` `// but no tau, so we can use the formula 2*pi to calculate it` ` ` `std::cout << ` `"The value of tau (using 2*pi) is: "` `<< M_PI * 2 << std::endl;` ` ` `return` `0;` `}` `// This code contributed by Ajax` |

## Java

`/*package whatever //do not write package name here */` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG {` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// java has no inbuilt tau but has inbuilt pi in math library` ` ` `// System.out.println(""+Math.PI); this print value` ` ` `// of pi` ` ` `// but no tau thus for using it we can use formula` ` ` `// for that` ` ` `System.out.println(` ` ` `"The value of tau (using 2*pi) is : "` ` ` `+ Math.PI * ` `2` `);` ` ` `}` `}` |

## Python3

`# Python code to demonstrate the working` `# of tau` `import` `math` `# Printing the value of tau using 2*pi` `print` `(` `"The value of tau (using 2*pi) is : "` `,end` `=` `"")` `print` `(math.pi` `*` `2` `)` `# Printing the value of tau using in-built tau function` `print` `(` `"The value of tau (using in-built tau) is : "` `,end` `=` `"")` `print` `(math.tau);` |

## C#

`using` `System;` `class` `GFG {` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `// C# has no inbuilt tau but has inbuilt pi` ` ` `// in Math library` ` ` `// Console.WriteLine(Math.PI); this print` ` ` `// value of pi` ` ` `// but no tau thus for using it we can use` ` ` `// formula for that` ` ` `Console.WriteLine(` `"The value of tau "` `+` ` ` `"(using 2*pi) is : {0}"` `,` ` ` `Math.PI * 2);` ` ` `}` `}` `// This code is contributed by surajrasr7277` |

**Output**

The value of tau (using 2*pi) is: 6.28319

**Time Complexity: **O(1)**Auxiliary Space: **O(1)**Note:** This code won’t work on Geeksforgeeks IDE as Python 3.6 is not supported. **Reference : **http://math.wikia.com/wiki/Tau_(constant)

This article is contributed by **Manjeet Singh**. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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