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Find the angle of Rotational Symmetry of an N-sided regular polygon
  • Last Updated : 31 Mar, 2021

Given an integer N which is the number of sides of a regular polygon. The task is to find the smallest angle of rotation such that the generated regular polygons have a similar position and dimensions, i.e. the new rotated polygon is in symmetry with the initial one.

A shape is said to have a rotation symmetry if there exists a rotation in the range [1, 360o] such that the new shape overlaps the initial shape completely.

Examples:  

Input: N = 4 
Output: 90 
Explanation: 
A 4 sided regular polygon is a square and when it is rotated by 90 degrees it results in the similar square.

Input: N = 8 
Output: 45 
 



Approach: For any N sided regular polygon, when rotated by 360 degrees, it aligns in the original position of the polygon. To find the minimum angle of rotation we use the property of symmetry of regular polygons. For an N sided regular polygon when rotated by 360/N degrees, the rotated polygon is in the same position as of the original polygon, which is the exterior angle of an N-sided regular polygon.

For example: 
Consider N = 4, 

Below is the implementation of the above approach. 

C++




// C++ program to find the angle
// of Rotational Symmetry of
// an N-sided regular polygon
 
#include <bits/stdc++.h>
using namespace std;
 
// function to find required
// minimum angle of rotation
double minAnglRot(int N)
{
    // Store the answer in
    // a double variable
    double res;
 
    // Calculating the angle
    // of rotation and type-
    // casting the integer N
    // to double type
    res = 360 / (double)N;
 
    return res;
}
 
// Driver code
int main()
{
    int N = 4;
    cout << "Angle of Rotational Symmetry: "
         << minAnglRot(N);
    return 0;
}

Java




// Java program to find the angle
// of Rotational Symmetry of
// an N-sided regular polygon
import java.io.*;
class GFG
{
 
// function to find required
// minimum angle of rotation
static double minAnglRot(int N)
{
    // Store the answer in
    // a double variable
    double res;
 
    // Calculating the angle
    // of rotation and type-
    // casting the integer N
    // to double type
    res = 360 / (double)N;
 
    return res;
}
 
// Driver code
public static void main (String[] args)
{
    int N = 4;
    System.out.println("Angle of Rotational Symmetry: " +
                                          minAnglRot(N));
}
}
 
// This code is contributed by shivanisinghss2110

Python3




# Python3 program to find the angle
# of Rotational Symmetry of
# an N-sided regular polygon
 
# Function to find required
# minimum angle of rotation
def minAnglRot(N):
     
    # Store the answer in a
    # variable
     
    # Calculating the angle
    # of rotation and type-
    # casting the integer N
    # to type
    res = 360 // N
 
    return res
 
# Driver code
if __name__ == '__main__':
     
    N = 4;
     
    print("Angle of Rotational Symmetry: ",
          minAnglRot(N))
 
# This code is contributed by mohit kumar 29   

C#




// C# program to find the angle
// of Rotational Symmetry of
// an N-sided regular polygon
using System;
class GFG
{
  
// function to find required
// minimum angle of rotation
static double minAnglRot(int N)
{
    // Store the answer in
    // a double variable
    double res;
  
    // Calculating the angle
    // of rotation and type-
    // casting the integer N
    // to double type
    res = 360 / (double)N;
  
    return res;
}
  
// Driver code
public static void Main (string[] args)
{
    int N = 4;
    Console.Write("Angle of Rotational Symmetry: " +
                                     minAnglRot(N));
}
}
  
// This code is contributed by rock_cool

Javascript




<script>
 
// Javascript program to find the angle
// of Rotational Symmetry of an N-sided
// regular polygon
 
// Function to find required
// minimum angle of rotation
function minAnglRot(N)
{
     
    // Store the answer in
    // a double variable
    let res;
 
    // Calculating the angle of
    // rotation and type-casting
    // the integer N to double type
    res = 360 / N;
 
    return res;
}
 
// Driver code
let N = 4;
 
document.write("Angle of Rotational Symmetry: " +
               minAnglRot(N));
 
// This code is contributed by divyeshrabadiya07
 
</script>
Output: 
Angle of Rotational Symmetry: 90

 

Time Complexity: O (1) 
Auxiliary Space: O (1)
 

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