Putting Algebraic Curves in Perspective

Ever wonder what happens when you combine graphing algebraic curves with drawing in perspective? The result uncovers some beautiful relationships between seemingly different shapes, and all because of what happens when you include infinity through projective geometry. This video was a project for MA 721 - Projective Geometry, as part of the Master of Science program in Mathematics at Emporia State University. Special thanks to Kevin Turner for assisting with post-production! References: * Ash, Avner, and Robert Gross. Elliptic Tales: Curves, Counting, and Number Theory. Princeton, NJ: Princeton University Press, 2014. * Brady, Zarathustra Elezar. “Cross Ratios.” MIT Mathematics. Accessed November 24, 2019. ~notzeb/. * Coxeter, H. S. M. Projective Geometry. New York: Springer, 2003. “Cross Ratio.” from Wolfram MathWorld. Accessed November 24, 2019. * Hisel, Jordan. “Addition Law on Elliptic Curves.“ 2014. * Leykin, Anton. “Systems of Polynomial Equations.” Lecture notes from MATH 4803: Introduction to Algebraic Computation. Accessed November 24, 2019. ~aleykin3/math4803spr13/BOOK/. * “Projectively Extended Real Numbers.” from Wolfram MathWorld. Accessed November 24, 2019. Image credits: * Albert Durer – Public Domain * Charles Rex Arbogast/AP, CC BY 2.0, @N06/25483324734 * Claudio Rocchini – Own work, CC BY-SA 3.0, : * Hans Vredeman de Vries – Public Domain * * Mikael Hvidtfeldt Christensen – Own work, CC BY 2.0, * new 1lluminati – Own work, CC BY 2.0, @N03/8358108650 * Theon – Own work, CC BY-SA 3.0, Music: DM Ashura vs. Enoch – Chaotic White