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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 ),
Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter. By Thales' theorem, this is a right triangle with right angle at B. Let the length of A′B be c n, which we call the complement of s n; thus c n 2 +s n 2 = (2r) 2. Let C bisect the arc from A to B, and let C′ be the ...
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 ...
In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
Three dimensional extent of an object m 3: L 3: extensive, scalar Volumetric flow rate: Q: Rate of change of volume with respect to time m 3 ⋅s −1: L 3 T −1: extensive, scalar Wavelength: λ: Perpendicular distance between repeating units of a wave m L: Wavenumber: k: Repetency or spatial frequency: the number of cycles per unit distance ...
A simple application of dimensional analysis to mathematics is in computing the form of the volume of an n-ball (the solid ball in n dimensions), or the area of its surface, the n-sphere: being an n-dimensional figure, the volume scales as x n, while the surface area, being (n − 1)-dimensional, scales as x n−1.
As a corollary of the chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4 The area of an annulus is determined by the length of the longest line segment within the annulus, which is the chord tangent to the inner circle, 2 d in the accompanying diagram.
Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as centre. In non-technical common usage it may mean the interior of the two-dimensional region bounded by a diameter and one of its arcs, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one.
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