All Modules

Minimal Surfaces & Soap Films

Discover why soap films find the shapes they do through 22 interactive demonstrations covering soap film physics, Plateau's problem, bubble mechanics, triply periodic surfaces, and the Weierstrass representation.

See also: Differential Geometry for the mean-curvature-zero condition that defines minimality, Optimization for the variational principle that surfaces minimize, and Geometric Flows for mean curvature flow as a path toward minima.

  1. 01

    Soap Film Physics

    Surface tension, energy minimization, and the physics of thin films

    3 demos
  2. 02

    Plateau's Problem

    Given a boundary curve, find the minimal surface — interactive wire frame solver

    3 demos
  3. 03

    Soap Bubbles & Constant Mean Curvature

    Pressure, double bubbles, and the isoperimetric problem

    3 demos
  4. 04

    Triply Periodic Minimal Surfaces

    The Gyroid, Schwarz P, and Schwarz D — infinite surfaces repeating in 3 directions

    4 demos
  5. 05

    The Weierstrass Representation

    Building minimal surfaces from complex analysis — the (g, η) construction

    3 demos
  6. 06

    Calculus of Variations

    The area functional, first variation, and why minimal surfaces are critical points

    3 demos
  7. 07

    Stability & Topology

    When minimal surfaces are stable, genus considerations, and the Costa surface

    3 demos

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