European Mathematics During the Renaissance

During the Renaissance, the rediscovery of philosophy, art and culture of the Ancient Greeks, together with introduction of Arabic art and science, and the desire of artists to represent the natural world realistically led them to study mathematics. Luca Pacioli and Leonardo da Vinci worked on the theory of perspective, golden ratio and algebra. Albrecht Durer developed exact drawing and worked on magic squares. With arithmetic and algebraic symbolics, theory of equation, imaginary and complex numbers, and plane and spherical trigonometry, mathematics during the Renaissance became the basis for all sciences, opening the era of modern high mathematics.

This class will be delivered online via the online platform Zoom. Enrolling students need to ensure they have an email, a reliable internet connection, microphone/speakers and access to a tablet, smartphone or computer.


  • Victor Katz. A history of mathematics, an introduction. NY: Harper Collins College Publishers, 1993.
  • Morris Kline. Mathematical thought from ancient to modern times. V 1. Oxford University Press, 1972.


  • Acquaintance with the history of mathematics of the Renaissance Europe.
  • Summary of arithmetic, geometry, proportions and proportionality by Luca Pacioli. Leonardo da Vinci’s drawing of regular polyhedra. Theory of perspective. German algebraists of the 16th c.
  • Algorithmus Demonstratus by the German scholar Regiomontanus. Introduction to the imaginary numbers for solution of cubic equations. Binomial coefficients. Irrational numbers.
  • Geronimo Cardano’s formula for solving cubic equations. Solving of equations of higher degrees by Francois Viete. Copernicus' development of trigonometry.

By the end of this course, students should be able to:

  1. Know the main concepts of the European mathematics during the Renaissance.
  2. Be familiar with the main figures of the eras: Luca Pacioli, Leonardo da Vinci, Nicholas of Cusa, Nicolas Chuquet, Gerolamo Cardano, Michael Stifel, Regiomontanus, Francois Viete, Nicolaus Copernicus and others.
  3. Understand the problems Renaissance mathematicians put forth and solved making it the basis for theory of variables, symbolic algebra, analytic geometry, differential and integral calculus.

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