Examples
Classical examples of minimal surfaces include:
- the plane, which is a trivial case
- catenoids: minimal surfaces made by rotating a catenary once around its directrix
- helicoids: A surface swept out by a line rotating with uniform velocity around an axis perpendicular to the line and simultaneously moving along the axis with uniform velocity
Surfaces from the 19th century golden age include:
- Schwarz minimal surfaces: triply periodic surfaces that fill R3
- Riemann's minimal surface: A posthumously described periodic surface
- the Enneper surface
- the Hennenberg surface: the first non-orientable minimal surface
Modern surfaces include:
- the Gyroid: One of Schoen's 1970 surfaces, a triply periodic surface of particular interest for liquid crystal structure
- the Saddle tower family: generalisations of Scherk's second surface
- Costa's minimal surface: Famous conjecture disproof. Described 1982 by Celso Costa and later visualized by Jim Hoffman. Jim Hoffman, David Hoffman and William Meeks III then extended the definition to produce a family of surfaces with different rotational symmetries.
- the Chen–Gackstatter surface family, adding handles to the Enneper surface.
Read more about this topic: Minimal Surface
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold peoples attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (18961966)