Pythagorean theorem
Teorema de Pitágoras
- Date
- c. 530 BCE · confidence medium
- Place
- Croton, Magna Graecia, Italy
- Credited to
- The Pythagorean school
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
In a right triangle, the square of the hypotenuse is the sum of the squares of the legs. It is the most proved theorem in history and the basis of Euclidean metric.
The relationship was known empirically to the Babylonians (Plimpton 322), in India (Sulba Sutras) and in China (the Gougu theorem) centuries earlier; the Greek contribution is the general proof.
What it led to
- the discovery of irrational numbers
- trigonometry
- analytic geometry
- Euclidean and Hilbert spaces
Built on
- Pythagorean triples of Plimpton 322c. 1800 BCE
- Egyptian geometry
Made possible
- Irrationality of the square root of 2c. 450 BCE
- Euclid Elements and the axiomatic methodc. 300 BCE
- land surveying
- navigation
- GPS and computational geometry