Blog
Explorations of fun calculus problems, Mathematica demos, and more.
Can You Bake the Optimal Cake Using Calculus?
Solving FiveThirtyEight's Riddler challenge: maximize the volume of a three-tiered cake that fits inside a cone using multivariable calculus.
Does a Lampshade Cast a Hyperbolic Shadow?
Using parametric plotting and Mathematica to prove that the shadow a lampshade casts on a wall traces out a pair of hyperbolas.
Modeling the Rolling Shutter Effect
Using Mathematica to simulate how a rolling shutter distorts a spinning propeller, from polar plots to contour plots to animated distortion.
The Riemann Sphere as a Stereographic Projection
Visualizing stereographic projection and the extended complex plane with an interactive Wolfram Demonstration. Explore how circles, lines, and curves in $\mathbb{C}$ lift to the Riemann sphere.
Parameterized Families of Elliptic Curves with Large Rational Torsion Subgroups
Exploring one-parameter families of elliptic curves with rational torsion points of order 4 through 12, with an interactive Wolfram Demonstration and connections to descent via isogeny.