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Tau – A Mathematical Constant

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  • Last Updated : 03 Feb, 2023
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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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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