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The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of dπ at the centre of the circle), each with an area of β 1 / 2 β · r 2 · dπ (derived from the expression for the area of a triangle: β 1 / 2 β · a · b · sinπ ...
An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2] V ≈ 4 π r 2 t , {\displaystyle V\approx 4\pi r^{2}t,}
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 ...
Fuel up with at least 2 grams of fiber per 1-cup serving: Fiber improves satiety and blood sugar regulation. If you find your soup is lower in fiber, simply stir in some canned beans or lentils.
Any two curves that have the same constant width are crossed by sets of lines with the same measure, and therefore they have the same length. Historically, Crofton derived his formula later than, and independently of, Barbier's theorem. [4] An elementary probabilistic proof of the theorem can be found at Buffon's noodle.
Donovan Dent had 17 points and eight assists, Nelly Junior Joseph added 16 points and 12 rebounds for his 45th career double-double, and New Mexico beat No. 22 UCLA 72-64 on Friday night in the ...
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