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Check whether two numbers are in golden ratio
  • Difficulty Level : Expert
  • Last Updated : 18 Dec, 2020

Given two numbers A and B, the task is to check that A and B are in the golden ratio.
Golden Ratio: Two numbers are said to be in the golden ratio if their ratio is the same as the ratio of the sum of the two numbers to the larger number. Here a > b > 0, Below is the geometric representation of the Golden ratio: 

\frac{A+B}{A} = \frac{A}{B} = \varphi = \frac{1+ \sqrt{5}}{2} = 1.618

Examples:  

Input: A = 1, B = 0.618
Output: Yes
Explanation:
These two numbers together forms Golden ratio

\frac{A}{B} = \frac{A + B}{A} = \frac{1.618}{1} = 1.618



Input: A = 61.77, B = 38.22

Output Yes

Explanation:

These two numbers together forms Golden ratio

\frac{A}{B} = \frac{A + B}{A} = \frac{99.99}{61.77} = 1.618

Approach: The idea is to find two ratios and check that this ratio is equal to the Golden ratio. That is 1.618.  

// Here A denotes the larger number

\frac{A}{B} = \frac{A + B}{A} = 1.618
 

Below is the implementation of the above approach:

C++




// C++ implementation to check 
// whether two numbers are in 
// golden ratio with each other
#include <bits/stdc++.h>
using namespace std;
 
// Function to check that two 
// numbers are in golden ratio
bool checkGoldenRatio(float a,
                      float b)
{
  // Swapping the numbers such 
  // that A contains the maximum
  // number between these numbers
  if(a <= b)
  {
    float temp = a;
    a = b;
    b = temp;
  }
 
  // First Ratio
  std::stringstream ratio1;
  ratio1 << std :: fixed <<
            std :: setprecision(3) <<
            (a / b);
 
  // Second Ratio
  std::stringstream ratio2;
  ratio2 << std :: fixed <<
            std :: setprecision(3) <<
            (a + b) / a;
 
  // Condition to check that two
  // numbers are in golden ratio
  if((ratio1.str() == ratio2.str()) &&
      ratio1.str() == "1.618")
  {
    cout << "Yes" << endl;
    return true;
  }
  else
  {
    cout << "No" << endl;
    return false;
  }
}
  
// Driver code
int main()
{
  float a = 0.618;
  float b = 1;
 
  // Function Call
  checkGoldenRatio(a, b);
 
  return 0;
}
 
// This code is contributed by divyeshrabadiya07

Java




// Java implementation to check 
// whether two numbers are in 
// golden ratio with each other
class GFG{
     
// Function to check that two 
// numbers are in golden ratio
public static Boolean checkGoldenRatio(float a,
                                       float b)
{
     
    // Swapping the numbers such 
    // that A contains the maximum
    // number between these numbers
    if (a <= b)
    {
        float temp = a;
        a = b;
        b = temp;
    }
     
    // First Ratio
    String ratio1 = String.format("%.3f", a / b);
     
    // Second Ratio
    String ratio2 = String.format("%.3f", (a + b) / a);
     
    // Condition to check that two
    // numbers are in golden ratio
    if (ratio1.equals(ratio2) &&
        ratio1.equals("1.618"))
    {
        System.out.println("Yes");
        return true;
    }
    else
    {
        System.out.println("No");  
        return false;
    }
}
 
// Driver code
public static void main(String []args)
{
    float a = (float)0.618;
    float b = 1;
     
    // Function Call
    checkGoldenRatio(a, b);
}
}
 
// This code is contributed by rag2127

Python3




# Python3 implementation to check
# whether two numbers are in
# golden ratio with each other
 
# Function to check that two
# numbers are in golden ratio
def checkGoldenRatio(a, b):
     
    # Swapping the numbers such
    # that A contains the maximum
    # number between these numbers
    a, b = max(a, b), min(a, b)
     
    # First Ratio
    ratio1 = round(a/b, 3)
     
    # Second Ratio
    ratio2 = round((a+b)/a, 3)
    # Condition to check that two
    # numbers are in golden ratio
    if ratio1 == ratio2 and\
       ratio1 == 1.618:
        print("Yes")
        return True
    else:
        print("No")
        return False
         
# Driver Code
if __name__ == "__main__":
    a = 0.618
    b = 1
     
    # Function Call
    checkGoldenRatio(a, b)

C#




// C# implementation to check 
// whether two numbers are in 
// golden ratio with each other
using System;
using System.Collections.Generic;
class GFG {
     
    // Function to check that two 
    // numbers are in golden ratio
    static bool checkGoldenRatio(float a,
                          float b)
    {
      // Swapping the numbers such 
      // that A contains the maximum
      // number between these numbers
      if(a <= b)
      {
        float temp = a;
        a = b;
        b = temp;
      }
      
      // First Ratio
      string ratio1 = String.Format("{0:0.000}", a / b);
      
      // Second Ratio
      string ratio2 = String.Format("{0:0.000}", (a + b) / a);
 
      // Condition to check that two
      // numbers are in golden ratio
      if(ratio1 == ratio2 && ratio1 == "1.618")
      {
        Console.WriteLine("Yes");
        return true;
      }
      else
      {
        Console.WriteLine("No");
        return false;
      }
    }
   
  // Driver code 
  static void Main() {
      float a = (float)0.618;
      float b = 1;
      
      // Function Call
      checkGoldenRatio(a, b);
  }
}
 
// This code is contributed by divyesh072019
Output: 
Yes

 

References: https://en.wikipedia.org/wiki/Golden_ratio 

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