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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 ...
In differential geometry, the sign of the area of a region of a surface is associated with the orientation of the surface. [7] The area of a set A in differential geometry is obtained as an integration of a density : μ ( A ) = ∫ A d x ∧ d y , {\displaystyle \mu (A)=\int _{A}dx\wedge dy,} where d x and d y are differential 1-forms that make ...
Surface area of a Dyson sphere with a radius of 1 AU 10 24: 1 yotta square meter (m 2) 1 square terametre (Tm 2) 1.9 Tm 2: Area swept by Jupiter's orbit around the Sun 6.4 Tm 2: Area swept by Saturn's orbit around the Sun 8.5 Tm 2: Surface area of the red supergiant star Betelgeuse: 10 25 24 Tm 2: Surface area of the hypergiant star VY Canis ...
The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.
A sphere is a surface that can be defined parametrically (by x = r sin θ cos φ, y = r sin θ sin φ, z = r cos θ) or implicitly (by x 2 + y 2 + z 2 − r 2 = 0). A surface is a two-dimensional object, such as a sphere or paraboloid. [55]
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A Rorschach test is a figure invariant by this symmetry, [203] as are butterfly and animal bodies more generally (at least on the surface). [204] Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea. [205] Fractals possess self-similarity. [206] [207]
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