minimal surface
The concept of 'minimal surface' arises in differential geometry and is crucial in understanding how surfaces behave under constraints such as minimal area and mean curvature.
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Definition
C1Differential Geometry
(technical, academic)A surface that locally minimizes its area and has zero mean curvature at every point.
Example
- A soap film spanning a wireframe forms a minimal surface.
- The study of minimal surfaces helps in understanding natural phenomena and structural design.
C2Calculus of Variations
(technical, academic)A surface that is a critical point of the area functional, meaning small deformations do not reduce its area.
Example
- In the calculus of variations, minimal surfaces are analyzed to find surfaces that optimize certain properties.
- Architects use principles of minimal surfaces to design efficient and aesthetically pleasing structures.
Similar
Terms that have similar or relatively close meanings to "minimal surface":