What's Minimal Surfaces

Definition : A minimal surface in R³ is a regular surface for which the mean curvature vanishes identically.

This is definition of Lagrange, who first defined minimal surface in 1760.
The more intuitive meaning of minimal surface is the surface of least area among a family of surfaces having the same boundary.

Helicoid to Catenoid

Helicoid and Catenoid are famous minimal surfaces.
Each other can transform this continuously .

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