Pythagorean Theorem - Geometric Dissection Proof
Explanation
This animation demonstrates a proof of the Pythagorean theorem using geometric dissection.
We start with a right triangle with vertical side a, horizontal side b, and hypotenuse c. Square a is divided into four polygons by drawing a line through its midpoint parallel to the hypotenuse, then drawing a perpendicular line also through the midpoint. These polygons are then rearranged around the perimeter of square c, while square b is transformed into a diamond shape that fits perfectly in the center.
This visually proves that a² + b² = c², which is the Pythagorean theorem.
Controls
Hypotenuse c: 5.00
About this Proof
This proof of the Pythagorean theorem uses geometric dissection, a technique where shapes are cut into pieces and rearranged to form other shapes.
By dividing square A into four quadrilaterals using lines parallel and perpendicular to the hypotenuse, and combining them with square B (which becomes a diamond in the center), we can exactly fill square C.
This visually demonstrates that a² + b² = c², providing an intuitive understanding of the theorem without relying on algebraic formulas.