This course examines the number 𝝅 from various points of view in pure and applied mathematics. Topics may include: (1) Geometry: Archimedes’ estimates; volume and surface area of spheres in arbitrary dimensions; Buffon’s needle (and noodle); Galperin’s colliding balls; the isoperimetric inequality; triangles in spherical and hyperbolic geometry; Descartes’s theorem on total angular defect (discrete Gauss-Bonnet). (2) Digit hunting: Viète’s infinite product; Wallis’s product and related ideas (the Gaussian integral and its multidimensional extension, saddle point approximation, Stirling’s approximation); the Leibniz-Gregory formula and Machin-type formulae; spigot algorithms and the Bailey-Borwein-Plouffe formula; elliptic integrals, the arithmetic-geometric mean, and the Brent-Salamin algorithm. (3) Analysis: complex exponentials; Fourier series; the Riemann zeta function, dilogarithms, Bernoulli numbers, and applications to number theory (means of arithmetic functions). (4) Algebra: the irrationality and transcendence of e and 𝝅.

Units: 1

Max Enrollment: 20

Prerequisites: MATH 302 or MATH 305; open to students with advanced background in physics, computer science, or related fields with permission of the instructor.

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall; Not Offered