triangle


Proofs of Pythagoras's Theorem
a²+b² = c²

Proof 1
In the diagram below the areas of the yellow and green squares add up to the area of the blue square. The two diagrams to the right illustrate how this must be so. Use your mouse to move any of the red points.

This proof is sometimes referred to as the Chinese square proof, or just the Chinese proof. It is supposed to have appeared in the Chou pei suan ching (ca. 1100 B.C.E.), according to Ralph H. Abraham who attributes this information to the book by Frank J. Swetz and T. I. Kao, Was Pythagoras Chinese?

This is not thought to be the earliest known proof however as the chinese text Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.) states and uses the Pythagorean theorem for surveying, astronomy, etc.