Pythagoras' Theorem

Friday, June 03, 2022

You might remember Pythagoras' theorem from high-school math:

In a right-angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides.

The following is a visual "proof" of the theorem:

(Continue scrolling to play the animation. Please use a smooth scrolling device like a touchscreen or a trackpad.)

Consider a right-angled triangle
with sides a, b, and c.
Make a square of side a + b.
Place 4 copies of the triangle in it.
They fit perfectly!
The visible blue is a square!
With side c.
Its area is .
Let's re-arrange the triangles
without changing the blue area...
Rotate two of the triangles by 90°.
What remains are two squares.
With sides a and b.
Their areas are and .
The rotations didn't change the blue area.
Therefore, c² = a² + b².

(@-me on twitter @kssreeram for comments and feedback.)