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.
#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 |
/*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 );
}
} |
# 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);
|
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 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));
|
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)