Pythagorean Triplets 🔺

This Python script generates exactly 10,000 Pythagorean triples using a mathematical method that ensures all generated triples satisfy the equation: a² + b² = c².

• Please note that it is almost completely useless.😁 This program is created because I was bored and wanted to make something funny lmao..

In a Pythagorean triple, a, b, and c represent the sides of a right-angled triangle, where a and b are the base and height and c is the hypotenuse.

How It Works 👷‍♂️

The script utilizes the following formula, based on two positive integers m and n (where m > n), to generate primitive Pythagorean triples:

• a = m² - n²
• b = 2 * m * n
• c = m² + n²

To ensure that a, b, and c form a valid Pythagorean triple, m and n must meet the following conditions:

1. m > n
2. m and n are coprime (i.e., their greatest common divisor is 1), and one of them is even.

After generating a primitive triple, the script produces non-primitive triples by multiplying the primitive triple by integer values k. This helps ensure that we generate enough triples to reach the goal of 10,000.

Code Flow ⏳

1. Triple Generation:

   • The script starts with m = 2 and increases m while iterating over valid values of n such that m > n.
   • It checks if m and n are coprime and that one of them is even before generating a valid triple.

2. Primitive and Non-Primitive Triples:

   • For each valid pair (m, n), the primitive triple is computed using the formula above.
   • The script then generates multiples of the primitive triple (non-primitive triples) until the list contains exactly 10,000 triples.

3. Output:

   • Once the script reaches 10,000 triples, it prints the results to the console. You can also limit the number of printed triples to a smaller number for easier viewing.

Installation

To run the script and generate 10,000 Pythagorean triples, simply execute it in your Python environment:

Installation 💻

1. Clone the Repository:

   git clone https://github.com/Saharsh000/Pythagorean_Triple_Generator.git
   cd Pythagorean_Triple_Generator

2. Run the Program:

python code.py

Customization

If you'd like to print a subset of the triples (for example, the first 10 triples), you can modify the print loop like this:

for triple in pythagorean_triples[:10]:
    print(triple)

Thank You 😄

• Well, thank you for reading.
• As always, if you have any issues with the program, you can contact me on discord(metagross2010ss) or email me.
• If you have liked this, please star the repo!! ⭐
• Have a nice day :D !!!! 👋