Pythagorean Theorem

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Geometric Proof

This animation is a visual proof of the Pythagorean theorem. The theorem states that the squared length of the hypotenuse of a right triangle is equal to the squared length of the two other sides added together. It's from this theorem that we get the common formula for distance $\sqrt{{\mathrm{𝝙x}}^2+{\mathrm{𝝙y}}^2}$ .

Explanation

At the beggining of the animation there are two square, one labeled a² and another labeled b². The first square has sides of length $a$ which means it has an area of $a\times a$ or $a^2$ and the other square has sides of length $b$ which means it has an area of $b^2$. Adding the area of both squares gives an area of $a^2+b^2$. At the end of the animation there is one square with sides of length $c$ which would give it an area of $c^2$. Since none of the triangles changed size or shape, this proves that $a^2+b^2=c^2$.

Desmos

A version of this proof made in Desmos.

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