History of the Pythagorean Theorem

By jukicselma1@gmail.com
  • 1900 BCE

    BABYLONIANS

    The oldest mention of the Pythagorean Theorem comes from the Babylonians, who recognized the relationship between the sides of a right triangle through clay tablets. Their understanding was practical, focusing on known integer triples rather than formal proof.
  • 1700 BCE

    INDIANS

    Ancient Indian had writings that mentioned geometric concepts similar to the Pythagorean Theorem, describing how to create a right-angled triangle with specific side lengths.
  • 500 BCE

    Pythagoras and the Pythagoreans

    Pythagoras, a Greek philosopher and mathematician, lived on the island of Samos during the years around 570 BCE. He is well-known for establishing the Pythagorean School, which combined elements of religion and philosophy. They were the first to formally prove the theorem. They recognized the relationship between the sides of a right triangle, expressed as a² + b² = c², with a and b as the legs and c as the hypotenuse.
  • 400 BCE

    PLATO

    Plato was presented ways of finding Pythagorean triples using algebra and geometry.
  • 300 BCE

    EUCLID

    The Greek mathematician Euclid provided a proof of the Pythagorean Theorem in his work, the Elements, specifically in Book I, Proposition 47. This geometric proof shows that the squares of the two shorter sides equal the square of the hypotenuse.
  • 200 BCE

    ARCHIMEDES

    The Greek mathematician Archimedes advanced geometry, in terms of areas and volumes, building on the Pythagorean Theorem
  • Period: 500 to 1200

    500 - 1200 CE

    Mathematicians in the Islamic world, including Al-Khwarizmi and Omar Khayyam, expanded on Greek geometric principles like the Pythagorean Theorem, with Khayyam providing a geometric proof. Meanwhile, Indian mathematicians like Bhaskara II offered more rigorous interpretations and contributed a proof using a clever square dissection.

  • Fermat's Last Theorem

    Fermat's Last Theorem generalized the Pythagorean theorem. He states that while there are infinite integer solutions to the Pythagorean Theorem a^2 + b^2 = c^2, there are no integer solutions to a^n + b^n = c^n for any integer bigger than 2.

  • Rene Descartes

    Rene Descartes used an algebraic approach to the Pythagorean Theorem expressing it through the distance formula in the Cartesian coordinate system and broadening its use.
  • Period: to

    Generalizations

    The Pythagorean Theorem is foundational in today's everyday life. It is utilized in construction, trigonometry, calculus, navigation, surveying, music, and physics.