001 : Gaussian Periods / Interactive mathematics
Arithmetic into
geometry.
A web app for exploring Gaussian periods: sums of roots of unity that reveal intricate patterns on the complex plane.
Launch web app (opens in a new tab)
The idea
Small rules. Unexpected patterns.
Start with evenly spaced points on the unit circle. Modular multiplication groups their exponents into orbits; adding the corresponding roots produces points on the complex plane. Changing the inputs reveals new symmetries, curves, and clusters.
The app pairs an interactive visualizer with step-by-step explanations of roots of unity, multiplicative grouping, and minimal polynomials. A gallery connects those ideas to the patterns they create.
From the visualizer
A closer look.
