This project uses Manim, a Python library for animations, to show a visual explanation of the inequality:

[ x + \frac{1}{x} \geq 2 \quad \text{(for all } x > 0\text{)} ]

1. It starts with a math assumption:
   ( x > 0 ) and ( x \geq \frac{1}{x} )

2. Then it draws a right triangle:

   • The base is 2 units long
   • The height is ( x - \frac{1}{x} )
   • The hypotenuse is calculated using the Pythagorean Theorem

3. The hypotenuse is transformed into a straight line showing ( x + \frac{1}{x} )

4. Finally, it compares that to 2, showing that the inequality is true.

It's like a visual proof using geometry, not just algebra.

Make sure you have Manim installed. You can install it using pip:

pip install manim
manim -pql animate_proof.py AnimateText