Pythagoras's Theorem

Pythagoras's theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:

$a^2 + b^2 = c^2$

This animation demonstrates a visual proof of the theorem through geometric transformation. The squares are rearranged and tessellated to show the fundamental relationship between the areas.

Interactive Diagram

Below is an interactive version of the final state of the animation. Use the sliders to change the values of a and b.

Explanation

The transparency of the squares allows you to see how they overlap and combine, with the color mixing revealing the geometric relationships. The tessellation demonstrates that the same shapes can tile the plane in multiple ways, preserving the area relationships described by the theorem.