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A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] 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 ...
This is a list of surfaces in mathematics. They are divided into minimal surfaces , ruled surfaces , non-orientable surfaces , quadrics , pseudospherical surfaces , algebraic surfaces , and other types of surfaces.
Endrass surface, a certain surface of degree 8 with 168 nodes; Sarti surface, a certain surface of degree 12 with 600 nodes; Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces
An open surface with x-, y-, and z-contours shown.. In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball.
In even more generality, arithmetic surfaces can be defined over Dedekind schemes, a typical example of which is the spectrum of the ring of integers of a number field (which is the case above). An arithmetic surface is then a regular fibered surface over a Dedekind scheme of dimension one. [2]
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