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

Javascript

// JavaScript has no inbuilt tau but has inbuilt pi in Math library
// console.log(Math.PI); // this prints the value of pi
// but no tau, so we can use the formula 2*pi to calculate it
console.log("The value of tau (using 2*pi) is: " + (Math.PI * 2));

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)
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