# Python Program for Pythagorean Quadruple

Given four points, the task is to check if the given four points form quadruple in python.

It is defined as a tuple of integers a, b, c, and d such that a2 + b2  + c2 = d2. They are, in fact, Diophantine Equations solutions. It represents a cuboid with integer side lengths |a|, |b|, and |c| and a space diagonal of |d| in the geometric interpretation.

Condition to check Quadruple = a2 + b2  + c2 = d2

where a, b, c, d are the given four points.

Examples:

Example1:

Input:

Given first point = 6
Given second point = 2
Given third point = 3
Given fourth point = 7

Output:

The given four points { 6 , 2 , 3 , 7 } forms a quadruple

Example2:

Input:

Given first point = 9
Given second point = 2
Given third point = 6
Given fourth point = 11

Output:

The given four points { 9 , 2 , 6 , 11 } forms a quadruple

## Program for Pythagorean Quadruple in Python

Below are the ways to check if the given four points form quadruple in python:

### Method #1: Using Mathematical Formula (Static Input)

Approach:

• Give the first number as static input and store it in a variable.
• Give the second number as static input and store it in another variable.
• Give the third number as static input and store it in another variable.
• Give the fourth number as static input and store it in another variable.
• Calculate the sum of squares of the given three numbers using the above given mathematical formula and store it in another variable.
• Check if the above result sum is equal to the square of the fourth number using the if conditional statement.
• If it is true, then print “The given four points forms a quadruple”.
• Else print “The given four points do not form a quadruple”.
• The Exit of the Program.

Below is the implementation:

# Give the first number as static input and store it in a variable.
p = 6
# Give the second number as static input and store it in another variable.
q = 2
# Give the third number as static input and store it in another variable.
r = 3
# Give the fourth number as static input and store it in another variable.
s = 7
# Calculate the sum of squares of the given three numbers using the above given
# mathematical formula and store it in another variable.
rslt_sum = p * p + q * q + r * r
# Check if the above result sum is equal to the square of the fourth number
# using the if conditional statement.
if (s * s == rslt_sum):
# If it is true, then print "The given four points forms a quadruple".
print("The given four points {", p, ",", q,
",", r, ",", s, "} forms a quadruple")
# Else print "The given four points do not form a quadruple".
else:
print("The given four points {", p, ",", q,
",", r, ",", s, "} do not form a quadruple")

# include <iostream>

using namespace std

int main() {
double p = 6
double q = 12
double r = 3
double s = 7
double rslt_sum = p * p + q * q + r * r
if ((s * s == rslt_sum)) {
cout << "The given four points {" << p << "," << q << "," << r << "," << s << "} forms a quadruple" << endl
}
else {
cout << "The given four points {" << p << "," << q << "," << r << "," << s << "} do not form a quadruple" << endl
}

}


Output:

The given four points { 6 , 2 , 3 , 7 } forms a quadruple

### Method #2: Using Mathematical Formula (User Input)

Approach:

• Give the first number as user input using the int(input()) function and store it in a variable.
• Give the second number as user input using the int(input()) function and store it in another variable.
• Give the third number as user input using the int(input()) function and store it in another variable.
• Give the fourth number as user input using the int(input()) function and store it in another variable.
• Calculate the sum of squares of the given three numbers using the above given mathematical formula and store it in another variable.
• Check if the above result sum is equal to the square of the fourth number using the if conditional statement.
• If it is true, then print “The given four points forms a quadruple”.
• Else print “The given four points do not form a quadruple”.
• The Exit of the Program.

Below is the implementation:

# Give the first number as user input using the int(input()) function and store it in a variable.
p = int(input("Enter some random number = "))
# Give the second number as user input using the int(input()) function and store it in another variable.
q = int(input("Enter some random number = "))
# Give the third number as user input using the int(input()) function and store it in another variable.
r = int(input("Enter some random number = "))
# Give the fourth number as user input using the int(input()) function and store it in another variable.
s = int(input("Enter some random number = "))
# Calculate the sum of squares of the given first three numbers using the above given
# mathematical formula and store it in another variable.
rslt_sum = p * p + q * q + r * r
# Check if the above result sum is equal to the square of the fourth number
# using the if conditional statement.
if (s * s == rslt_sum):
# If it is true, then print "The given four points forms a quadruple".
print("The given four points {", p, ",", q,
",", r, ",", s, "} forms a quadruple")
# Else print "The given four points do not form a quadruple".
else:
print("The given four points {", p, ",", q,
",", r, ",", s, "} do not form a quadruple")


Output:

Enter some random number = 9
Enter some random number = 2
Enter some random number = 6
Enter some random number = 11
The given four points { 9 , 2 , 6 , 11 } forms a quadruple