Finding Square Root of a Number

I practiced using the bisection method in Python to find square root of a number automatically.

Personal Tweak

This project is based on the FreeCodeCamp (FCC) Scientific Computing with Python curriculum. I added the input() function to let users add the number theirself.

Features

• Safety First: It has a built-in guard (the ValueError) that stops the code immediately if you try to find the square root of a negative number, which isn't possible in real numbers.
• Instant Shortcuts: It doesn't waste energy on obvious math. If you ask for the root of 0 or 1, it just gives you the answer instantly.
• Adjustable Precision: Using tolerance, you can decide exactly how accurate you want the answer to be. By default, it stops once it's within 0.0000001 of the true value.
• Anti-Loop Protection: The max_iterations acts like a safety timer. If the math gets too complicated and the code can't find a perfect answer quickly, it quits instead of freezing your computer lol

Project Structure

Inside this repository, you will find:

• bisection.py — The main Python script.
• README.md — The documentation you are reading right now.

How It Works (The Logic)

The core of this is the Bisection Method, which is just a fancy way of saying "splitting things in half until you get it right."

1. Setting the Boundaries: The code starts by picking a range where the answer could be. It sets low at 0 and high at the number you entered.

2. The Guessing Game: It picks the middle point (mid) between low and high. And to see if the guess is right, the code squares it (mid**2). It then calculates the "gap" between that result and your target number.

3. Checking the "Gap": This is where abs() comes in. It checks the gap between its guess and the real answer. If that gap is smaller than your tolerance (0.0000001), it shouts "Found it!" and stops.

4. Narrowing the Search: If the gap is still too big, the code makes a choice :

   • If the guess was too low, it moves the low boundary up to the middle.
   • If the guess was too high, it moves the high boundary down to the middle.

5. Repeat: It keeps cutting the search area in half over and over again. It keeps going until it either hits the target or runs out of max_iterations.

Output Example

For an example, I want to find the square root of 16:

Enter your number to find the square root: 16
The square root of 16 is approximately 4.0

How about something even more complex? In this case I want to find the square root of 189.45:

Enter your number to find the square root: 189.45
The square root of 189.45 is approximately 13.764083696853774

• NOTE! The output shows high decimal precision because the algorithm prioritizes accuracy based on a 1e-7 tolerance level. It's math in its rawest form :)