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