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Check whether two numbers are in silver ratio
  • Last Updated : 16 Apr, 2021

Given two numbers A and B, the task is to check that A and B are in silver ratio.

Silver Ratio: Two numbers are said to be in silver ratio if the ratio of the sum of the smaller and twice the larger number to the larger number is the same as the ratio of the larger one to the smaller one. Below is the representation of the silver ratio:

\frac{2*A+B}{A} = \frac{A}{B} = \delta_{\varsigma} = {1+ \sqrt{2}} = 2.414
 

for A > 0, B > 0

 



Examples:

Input: A = 2.414, B = 1 
Output: Yes 
Explanation:

\frac{A}{B} = 2.414 \;\;\text{as well as}\;\; \frac{2*A + B}{A} = \frac{2.414}{1} = 2.414
 

Input: A = 1, B = 0.414 
Output No 
Explanation: Ratio of A to B do not form a golden ratio

 

Approach: The idea is to find two ratios and check whether they are equal to the silver ratio(2.414).

// Here A denotes the larger number
\frac{A}{B} = \frac{2*A + B}{A} = 2.414

Below is the implementation of the above approach:

C++




// C++ implementation to check
// whether two numbers are in
// silver ratio with each other
#include<bits/stdc++.h>
using namespace std;
 
// Function to check that two
// numbers are in silver ratio
bool checksilverRatio(float a, float b)
{
     
    // Swapping the numbers such
    // that A contains the maximum
    // number between these numbers
    if(a < b)
        swap(a, b);
     
    // First Ratio
    float ratio1 = ((a / b) * 1000.0) / 1000.0;
     
    // Second Ratio
    float ratio2 = (int)(((2 * a + b) /
                          a) * 1000);
    ratio2 = ratio2 / 1000;
     
    // Condition to check that two
    // numbers are in silver ratio
    if (ratio1 == ratio2 &&
       (int)(ratio1 - 2.414) == 0)
    {
        cout << "Yes\n";
        return true;
    }
    else
    {
        cout << "No\n";
        return false;
    }
}
 
// Driver Code
int main()
{
    float a = 2.414;
    float b = 1;
     
    // Function call
    checksilverRatio(a, b);
}
 
// This code is contributed by ishayadav181

Java




// Java implementation to check
// whether two numbers are in
// silver ratio with each other
import java.util.*;
import java.lang.*;
 
class GFG{
 
// Function to check that two
// numbers are in silver ratio
static boolean checksilverRatio(double a,
                                double b)
{
 
    // Swapping the numbers such
    // that A contains the maximum
    // number between these numbers
    if (a < b)
    {
        a = a + b;
        b = a - b;
        a = a - b;
    }
 
    // First Ratio
    double ratio1 = ((a / b) * 1000) / 1000;
 
    // Second Ratio
    double ratio2 = (int)(((2 * a + b) /
                           a) * 1000);
    ratio2 = ratio2 / 1000;
 
    // Condition to check that two
    // numbers are in silver ratio
    if (ratio1 == ratio2 &&
       (int)(ratio1 - 2.414) == 0)
    {
        System.out.println("Yes");
        return true;
    }
    else
    {
        System.out.println("No");
        return false;
    }
}
 
// Driver Code
public static void main(String[] args)
{
    double a = 2.414;
    double b = 1;
 
    // Function call
    checksilverRatio(a, b);
}
}
 
// This code is contributed by jana_sayantan

Python3




# Python3 implementation to check
# whether two numbers are in
# silver ratio with each other
 
# Function to check that two
# numbers are in silver ratio
def checksilverRatio(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((2 * a + b)/a, 3)
    # Condition to check that two
    # numbers are in silver ratio
    if ratio1 == ratio2 and\
       ratio1 == 2.414:
        print("Yes")
        return True
    else:
        print("No")
        return False
         
# Driver Code
if __name__ == "__main__":
    a = 2.414
    b = 1
     
    # Function Call
    checksilverRatio(a, b)

C#




// C# implementation to check
// whether two numbers are in
// silver ratio with each other
using System;
 
class GFG{
 
// Function to check that two
// numbers are in silver ratio
static bool checksilverRatio(double a,
                             double b)
{
 
    // Swapping the numbers such
    // that A contains the maximum
    // number between these numbers
    if (a < b)
    {
        a = a + b;
        b = a - b;
        a = a - b;
    }
 
    // First Ratio
    double ratio1 = ((a / b) * 1000) / 1000;
 
    // Second Ratio
    double ratio2 = (int)(((2 * a + b) /
                        a) * 1000);
    ratio2 = ratio2 / 1000;
 
    // Condition to check that two
    // numbers are in silver ratio
    if (ratio1 == ratio2 &&
       (int)(ratio1 - 2.414) == 0)
    {
        Console.WriteLine("Yes");
        return true;
    }
    else
    {
        Console.WriteLine("No");
        return false;
    }
}
 
// Driver Code
public static void Main()
{
    double a = 2.414;
    double b = 1;
 
    // Function call
    checksilverRatio(a, b);
}
}
 
// This code is contributed by sanjoy_62

Javascript




<script>
 
// Javascript Program to check
// whether two numbers are in
// silver ratio with each other
 
// Function to check that two
// numbers are in silver ratio
function checksilverRatio(a, b)
{
   
    // Swapping the numbers such
    // that A contains the maximum
    // number between these numbers
    if (a < b)
    {
        a = a + b;
        b = a - b;
        a = a - b;
    }
   
    // First Ratio
    let ratio1 = ((a / b) * 1000) / 1000;
   
    // Second Ratio
    let ratio2 = Math.floor(((2 * a + b) /
                           a) * 1000);
    ratio2 = ratio2 / 1000;
   
    // Condition to check that two
    // numbers are in silver ratio
    if (ratio1 == ratio2 &&
       (ratio1 - 2.414) == 0)
    {
        document.write("Yes");
        return true;
    }
    else
    {
        document.write("No");
        return false;
    }
}
 
// Driver Code
  let a = 2.414;
    let b = 1;
   
    // Function call
    checksilverRatio(a, b);
     
    // This code is contributed by chinmoy1997pal.
</script>
Output: 
Yes

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

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