What is the most elegant proof of the Pythagorean theorem? [closed]
Solution 1:
I really like this one (image taken from cut-the-knot #4)
along with
$$(a+b)^2 = 4\cdot\frac{1}{2}a b + c^2$$ $$\Leftrightarrow c^2 = a^2 + b^2$$
It's so clear and easy ...
Note: Just to make it clear, the side of the square is a+b
Solution 2:
The proof that uses the fact that shearing a parallelogram parallel to one of its sides preserves area is my favorite. Here's an animation from this site:
