History of Quadratic Equations

By Rachel Fisher
  • 3100 BCE

    Unification of the Egyptian Empire

    Unification of the Egyptian Empire
  • 2300 BCE

    Town of Babylon was founded

    Town of Babylon was founded
    The town of Babylon, located in modern-day Iraq, was founded by ancient Akkadian-speaking people of southern Mesopotamia.
  • 2000 BCE

    Babylonians Solved Quadratic Equations

    Babylonians Solved Quadratic Equations
    Using a geometric method of completing the square, Babylonians moved pieces of rectangles and squares to solve. They needed a method of finding how much to increase the size of their fields to pay the tax collector.
  • 1800 BCE

    Egyptian Geometric Tables

    Egyptian Geometric Tables
    Egyptian engineers, scribes, and priests kept tables for all possible sides and shapes of squares and rectangles. Evidence that ancient Egyptians could solve some quadratic equations was recorded on the Berlin Papyrus.
  • 1792 BCE

    Ammorite King Hammurabi ruled Babylonia

    Ammorite King Hammurabi ruled Babylonia
    1792-1750 BCE
    King Hammurabi brought central and southern Mesopotamia under Babylonian rule.
    After his death, the Babylonian empire reverted to several small kingdoms.
  • 642 BCE

    Muslims conquered ancient Egypt

    Muslims conquered ancient Egypt
    Arab invasion led by ʿAmr ibn al-ʿĀṣ in AD 639–642
  • 539 BCE

    The Fall of Babylon

    The Fall of Babylon
    Cyrus the Great (Persian king) conquered Babylon
  • 500 BCE

    Pythagoras

    Pythagoras
    Pythagoras used geometry, and refused to allow that ratios of the area of squares and the length of their sides could be anything other than rational.
  • 332 BCE

    Egyptian Empire fell to Alexander the Great

    Egyptian Empire fell to Alexander the Great
  • 300 BCE

    Euclid Solved Quadratic Equations

    Euclid Solved Quadratic Equations
    Using a strictly geometric approach, Euclid found a general procedure to solving quadratics. He concluded that irrational numbers exist.
  • 628

    Brahmagupta understood negative numbers

    Brahmagupta understood negative numbers
    Indian mathematician Brahmagupta's understanding of negative numbers allowed for solving quadratic equations with two solutions, one possibly negative.
  • 825

    Muhammad ibn Mūsa al-Khwārīzmī solved quadratics by completing the square

    Muhammad ibn Mūsa al-Khwārīzmī solved quadratics by completing the square
    Mathematicians of al-Khwārīzmī’s time did not employ the concept of negative numbers, so Muhammad ibn Mūsa al-Khwārīzmī did not use negative coefficients or accept negative solutions.
  • 900

    Sridhara gave a formula for solving Quadratic Equations

    Sridhara gave a formula for solving Quadratic Equations
    We know about Sridhara through the writings of Bhaskara II, also an Indian mathematician. He was one of the first to give a formula for solving quadratic equations. His formula was very close to the derivation of the quadratic formula that we use.
  • 1100

    Bhaskara II discovered that any positive number has two square roots

    Bhaskara II discovered that any positive number has two square roots
    Bhaskara II demonstrated that the quadratic equation has two roots by discovering that any positive number (the discriminant of the quadratic formula) has two square roots.
  • 1145

    Abraham bar Hiyya brought the Quadratic Formula to Europe

    Abraham bar Hiyya brought the Quadratic Formula to Europe
    "Abraham bar Hiyya's book, Treatise on Measurement and Calculation, is the earliest Arab algebra book in Europe. It contains the complete solution of the general quadratic. 1145 was also the year that al-Khwarizmi's book was translated." O'Connor, JJ, and EF Robertson. “Abraham Bar Hiyya - Biography.” Maths History, Nov. 1999, mathshistory.st-andrews.ac.uk/Biographies/Abraham/.
  • 1300

    European Renaissance began

    European Renaissance began
    People embraced education, classical arts, science, mathematics, and literature.
  • 1545

    Girolamo Cardano compiled the quadratic works (Italy)

    Girolamo Cardano compiled the quadratic works (Italy)
    He combined Al-Khwarismi's solution with Euclid's geometric solution. He also acknowledged the existence of imaginary numbers (roots of negative numbers).
  • 1564

    William Shakespeare was born

    William Shakespeare was born
    Shakespeare is often considered "the greatest dramatist" of all time" (Biography.com, 2019)

  • Viete wrote general forms of equations (France)

    Viete wrote general forms of equations (France)
    Viete used vowels to represent unknowns in equations and consonants to represent known quantities. By using letters to represent known and unknown quantities, he was able to write general forms of equations, rather than relying on specific examples.

  • Descartes introduced modern algebraic notation (France)

    Descartes introduced modern algebraic notation (France)
    Descartes wrote La Gèometrie, which introduced the convention where letters near the beginning of the alphabet represent known quantities and letters near the end represent unknowns. The quadratic formula adopted the form as we know it today.

  • United States Declared Independence from Great Britain

    United States Declared Independence from Great Britain
    On July 4, 1776, the Continental Congress voted to adopt the Declaration of Independence

  • Po-Shen Loh found a simpler way to solve quadratic equations (Pittsburgh)

    Po-Shen Loh found a simpler way to solve quadratic equations (Pittsburgh)
    Loh, a mathematician at Carnegie Mellon University, discovered a simple method for solving quadratic equations without using the quadratic formula.