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Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.
Berger–Kazdan comparison theorem (Riemannian geometry) Bernstein's theorem (approximation theory) Bernstein's theorem (functional analysis) Berry–Esséen theorem (probability theory) Bertini's theorem (algebraic geometry) Bertrand–Diquet–Puiseux theorem (differential geometry) Bertrand's ballot theorem (probability theory, combinatorics)
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PGA allows projection, meet, and angle formulas to be derived from (,,) - with a very minor extension to the algebra it is also possible to derive distances and joins. PGA is a widely used system that combines geometric algebra with homogeneous representations in geometry, but there exist several other such systems.
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The given formula is for the plane passing through the center of mass, which coincides with the geometric center of the cylinder. If the xy plane is at the base of the cylinder, i.e. offset by d = h 2 , {\displaystyle d={\frac {h}{2}},} then by the parallel axis theorem the following formula applies:
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 ...