The Pythagorean theorem

3 min read

Interactive Visualization

• You can drag and drop the side squares into the hypotenuse (purple) square.
• You can rotate the squares.
• You can click on them to break them in unit squares and drag them into the hypotenuse square.
• Use the Reset button on the top left corner to reset the puzzle.

The Theorem

It states that in any right-angled triangle, the area of the square built on the hypotenuse ($c$) is equal to the sum of the areas of the squares on the other two sides ($a$ and $b$). Mathematically, it is expressed as:

In the example above, the values of $a$, $b$, and $c$ are 3, 4, and 5 respectively, which satisfies the equation:

Fascinating Facts You Might Not Know

Pythagoras Didn’t Discover It

Babylonian tablets (like Plimpton 322) and ancient Indian and Chinese texts prove that civilizations were using Pythagorean triples over 1,000 years before Pythagoras was even born. He was simply the first credited with proving it generally.

There are Hundreds of Proofs

The Pythagorean theorem is one of the most proved theorems in all of mathematics, with over 300 unique proofs recorded. Former U.S. President James A. Garfield even published an original proof using a trapezoid in 1876.

It Powers Modern GPS & 3D Graphics

Every time your phone calculates the distance between two locations or a rendering engine projects a 3D video game onto a 2D screen, it is running multidimensional variations of $a^2 + b^2 = c^2$ in the background.