Change the lengths of the two legs a and b that form the right angle. Add the areas of the squares drawn on each leg (a², b²), and it's always exactly equal to the area of the square drawn on the hypotenuse (c²). This is the Pythagorean theorem, a² + b² = c².
The Pythagorean theorem is one of the most famous formulas in math. In a right triangle, square the lengths of the two legs that form the right angle (a, b) and add them, and you always get the same value as the square of the hypotenuse's length (c): a²+b²=c². Remarkably, people in ancient Babylon and Egypt already knew this relationship and used it in daily life, long before Pythagoras.
In ancient Egypt, they tied knots in a rope at 3:4:5 intervals to make a right angle. These three lengths (3, 4, 5) satisfy 3²+4²=5² exactly (9+16=25). The same principle is still used today in construction and woodworking to check for a right angle.
Change the lengths of a and b with the sliders and see with your own eyes that the sum of the two square areas always equals the area of the square on the hypotenuse.