Historical background

Many proofs of Pythagoras’s Theorem are known. The ones in this resource span a period of over 2000 years.

Approach 1

This starting point can lead to at least two different proofs. One of them is quite probably Pythagoras’s original argument;1 Pythagoras lived from about 569-475 BCE.

This approach is developed further in The Quintessential Proof.

Approach 2

This is due to Bhaskara (1114-1185), also known as Bhaskaracharya, an Indian mathematician and astronomer of great reknown.

Approach 3

This is due to James A. Garfield (1831-1881), who was the 20th president of the United States of America.

Approach 4

This argument appears in Euclid’s Elements, Book I, Proposition 47. Euclid lived from about 325-265 BCE, and according to Proclus (a later Greek mathematician, 411-485 CE), this proof of Pythagoras’s Theorem is due to Euclid himself.2

  1. Heath, Thomas L., Euclid: The thirteen books of the elements, 2nd. ed, Cambridge 1926 (reprinted by Dover, 1956), vol. 1, pp. 353-354.

  2. ibid.