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maximum surface area - translation to russian
![[[Schwarz lantern]] with <math>M</math> axial slices and <math>N</math> radial vertices. The limit of the area as <math>M</math> and <math>N</math> tend to infinity doesn't converge. In particular it doesn't converge to the area of the cylinder.](https://commons.wikimedia.org/wiki/Special:FilePath/Schwarz-lantern.gif?width=200 "[[Schwarz lantern]] with <math>M</math> axial slices and <math>N</math> radial vertices. The limit of the area as <math>M</math> and <math>N</math> tend to infinity doesn't converge. In particular it doesn't converge to the area of the cylinder.")
![cylinder]] of the same height and radius.](https://commons.wikimedia.org/wiki/Special:FilePath/Archimedes sphere and cylinder.svg?width=200 "cylinder]] of the same height and radius.")
![sectors]] which rearrange to form an approximate [[parallelogram]].](https://commons.wikimedia.org/wiki/Special:FilePath/CircleArea.svg?width=200 "sectors]] which rearrange to form an approximate [[parallelogram]].")
![A square metre [[quadrat]] made of PVC pipe.](https://commons.wikimedia.org/wiki/Special:FilePath/SquareMeterQuadrat.JPG?width=200 "A square metre [[quadrat]] made of PVC pipe.")
- closed area
- controlled area
- controlled access area
- fenced area
- fingerprint pattern area
- high risk area
- inaccessible area
- key area
- limited area
- logically protected area
- monitored area
- physically protected area
- protected area
- restricted area
- secret area
- secure area
- secure storage area
- security-sensitive area
- survey area
- target area
- user area
Wikipedia
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.
