Pythagorean Theorem Proof by Transformation
- Bill Lombard
Pythagorean Theorem Proof by Transformation There are three stages: 1- For 0<n<1, a² and b² are sheared parallel to their sides to become parallelograms. 2- For 1<n<2, these parallelograms are translated downward. 3- For 2<n<3, the parallelograms are sheared to become rectangles whose areas sum to c². Point C can be moved to create different values of a and b. - credits to: https://www.youtube.com/watch?v=cLW6ZiZvAnM
Why do the two squares maintain their area when sheared into parallelograms? Why do the two parallelograms maintain their area when sheared into rectangles?