Interactive geometry / 06

The 5:1 Ellipse

Geometry

An ellipse with a constant semi-major axis a rotates about its centre, while its semi-minor axis b oscillates between two values at n cycles per revolution.

b(θ) = (b₁+b₂)/2 + (b₂−b₁)/2 · cos(n·θ)

The orange locus is the path of the minor-axis tip over one full turn — an n-petal flower when n is a whole number.

Shape & motion

Semi-major axis a Minor axis lower b₁ Minor axis upper b₂ Cycles per revolution n Rotation speed Line width Accent colour Auto-sweep first slider

Saved PNGs

PNG captures are named with their parameter values. Commit the downloaded files to the repo and they will appear here automatically (fetched via the GitHub API).