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Prodigi

Dance, Phosphor Fine Art Print

Dance, Phosphor Fine Art Print

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A minimal surface is a mathematical abstraction of a soap film.

The catenoid is the surface of rotation swept by revolving the hyperbolic cosine graph x=coshz about the z-axis. The catenoid is minimal. Inversely, it has been known since the 18th century that (up to scaling) the catenoid is the only "complete" non-planar minimal surface of rotation.

The helicoid is the surface swept by a line L orthogonal to the z-axis in three-space if we rotate L at unit angular speed about the z-axis while simultaneously translating L at unit speed along the z-axis. Mathematicians call the helicoid a "ruled" surface because it is a union of lines. The helicoid is minimal. Inversely, it has been known since the 18th century that (up to scaling) the helicoid is the only "complete" non-planar minimal ruled surface.

Remarkably, one full turn of the helicoid can be wrapped around the catenoid without stretching or folding; there is a "local isometry" from the helicoid onto the catenoid.

More is true: The catenoid and helicoid are the real and imaginary parts of an abstract circular family of surfaces in complex three-space. When this family is projected to real three-space by rotating through the complex circle parameter and taking the real part, we get the family of minimal surfaces shown.

Printed on museum-quality fine art print paper (200 gsm) with a textured, matte finish.

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