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Historical Timeline of Cubic Equations

By lreyes
  • 4000 BCE

    Babylonian Tablet

    Babylonian Tablet
    The Babylonians solved cubic equations with the help of tables (Allen, n.d).
  • 1247 BCE

    Quin Jiushao Solves Cubic Equations in The Shushu Jiuzhang

    Quin Jiushao Solves Cubic Equations in The Shushu Jiuzhang
    In the book Shushu Jiuzhang, perhaps the most brilliant Chinese mathematician of this time was Qin Jiushao, a rather violent and corrupt imperial administrator and warrior, who explored solutions to quadratic and even cubic equations using a method of repeated approximations (The Story of Mathematics, n.d.).
  • 1180 BCE

    Al-muʿādalāt Included Work on Cubic Equations

    Al-muʿādalāt Included Work on Cubic Equations
    Sharaf al-Dīn al-Ṭūsī in his book Al-muʿādalāt included a work devoted to the solution of cubic equations (Berggren & Sharaf Al-Dīn, 1990). (Image from Qatar Digital Library. (2015, May 22). al-Muʿādalāt المعادلات [‎66v] (63/290). Retrieved June 6, 2020, from https://www.qdl.qa/en/archive/81055/vdc_100044790015.0x00008e).
  • 1150 BCE

    Baskara II Contributed to Finding Solutions to Cubic Equation

    Baskara II Contributed to Finding Solutions to Cubic Equation
    Some of Bhaskara's contributions to mathematics include in Lilavati, solutions of quadratic, cubic and quartic indeterminate equations (New World Encyclopedia, n.d.).
  • 1131 BCE

    Omar Khayyam Provides Examples of Cubic Equations

    Omar Khayyam Provides Examples of Cubic Equations
    Omar Khayyám, made significant progress in developing the theory of cubic equations and published his findings in Treatise on Demonstration of Problems of Algebra (McKay, n.d.).
  • 626 BCE

    Jigu Suanjing Contains 25 Solved Cubic Functions

    Jigu Suanjing Contains 25 Solved Cubic Functions
    Wang Xiaotong, established and solved 25 cubic equations (McKay, n.d).
  • 560 BCE

    Archimedes Solves Cubic Equations

    Archimedes Solves Cubic Equations
    Archimedes, in his monumental work The Sphere and Cylinder,
    considers the problem of cutting a sphere by a plane so that the
    two segments shall have a given ratio; this leads to a cubic
    equation solution(The University of Colorado Denver, n.d.).
  • 430 BCE

    Hippocrates Reduced Duplicating the Cube

    Hippocrates Reduced Duplicating the Cube
    Hippocrates of Chios reduced
    duplicating the cube to a problem in mean proportionals (Brown University, 2018).
  • 350 BCE

    Reduction of Cube Inspires Conics

    Reduction of Cube Inspires Conics
    Menaechmus’ work in conic; where the greeks were aware of methods to solve certain cubic equations using
    intersecting conics, but did not consider general cubic equations because their framework was too influenced by geometry (Brown University, 2018).
  • 150 BCE

    Jaina Mathematics

    Jaina Mathematics
    The main topics of Jaina mathematics in around 150 BC were: the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations (MacTutor, n.d.).
  • 1225

    Fibonacci Finds Solution to Cubic Equation

    Fibonacci Finds Solution to Cubic Equation
    Fibonacci computed the positive solution to x^3 + 2 x^2 + 10x = 20 to 8 decimal places (although he gives his solution in sexagesimal) (Brown, 2018).
  • 1526

    Ferro Reveals Solution for Depressed Cubic Equation

    Ferro Reveals Solution for Depressed Cubic Equation
    Scipione del Ferro (1465-1526), who solved the depressed cubic equation (Brown, 2018).
  • 1530

    Tartaglia Claims Solution to Two Cubics

    Tartaglia Claims Solution to Two Cubics
    In 1530, another Italian named Tartaglia claimed a solution to two cubics presented by Zuanne da Coi (Brown, 2018).
  • 1545

    Cardano Publishes Tartaglia's Work

    Cardano Publishes Tartaglia's Work
    Cardano learned that Tartaglia’s work was known to del Ferro, he
    broke the agreement and published Ars Magna in 1545 (Brown, 2018). He proposed a method for solving cubic equations, which is now known today as Cardano’s method (McKay, n.d.).
  • 1548

    Ferrari Better and Bested Tartaglia in the Debate

    Ferrari Better and Bested Tartaglia in the Debate
    Tartaglia then challenged Cardano, who declined and the challenge eventually passed to Ferrari. Ferrari understood cubics better and bested Tartaglia at his own game (Brown, 2018).

  • Francois Viete Derived the Trigonometric Solution for The Cubic Equation

    Francois Viete Derived the Trigonometric Solution for The Cubic Equation
    François Viète, known as the father of modern algebraic notation, derived the trigonometric solution for the cubic equation with three real roots (McKay, n.d.).

  • Rene Descartes Extended Viete's Study

    Rene Descartes Extended Viete's Study
    René Descartes, a French philosopher, mathematician, and scientist and dubbed the father of modern Western philosophy, summarized and extended Viète’s study (McKay, n.d.).

  • Present Application of Cubic Equation

    The cubic equation is utilized for volume, measurements, and other applications. Some other applications of cubic functions or equations are found in the fields of physics, chemistry, economics, or additional areas of mathematics (McKay, n.d.).