Philadelphia Area Seminar History of Mathematics PASHoM

Thursday, January 16, 2025 - 6:30pm to 8:00pm

Professor David Richeson

Dickinson College; Chair of the Department of Mathematics and Computer Science

The elegant heart-shaped cardioid is one of the most beloved curves in mathematics. In this talk, we discuss the history of this curve, its many interesting geometric properties, and the many places where the curve appears—as an epicycloid, as an envelope of lines, as the envelope of circles, as the caustic in the bottom of your coffee cup, in the Mandelbrot set, in the mechanics of certain drawbridges, in the design of microphones, and more. As we shall see, analyzing the curve will require a deep mathematical toolkit containing geometry, algebra, analytic geometry, multivariable calculus, trigonometry, abstract algebra, complex dynamics, origami, and more. We also discuss some recent developments.