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The diameter is the maximum distance between any pair of convex hull vertices found as the two points of contact of the parallel lines in this sweep. The time for this method is dominated by the time for constructing the convex hull: O ( n log n ) {\displaystyle O(n\log n)} for a finite set of n {\displaystyle n} points, or time O ( n ...
Any physically meaningful equation, or inequality, must have the same dimensions on its left and right sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations.
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 ...
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 ),
Although named for Edgar Buckingham, the π theorem was first proved by the French mathematician Joseph Bertrand in 1878. [1] Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains, in distinct terms, all the basic ideas of the modern proof of the theorem and clearly indicates the theorem's utility for modelling physical phenomena.
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 ...
Jung's theorem provides more general inequalities relating the diameter to the radius. [5] The isodiametric inequality or Bieberbach inequality, a relative of the isoperimetric inequality, states that, for a given diameter, the planar shape with the largest area is a disk, and the three-dimensional shape with the largest volume is a sphere.
diameter D radius R ... (θ) and s – (θ) are the roots for s of the equation ... Ball (mathematics), the usual term for the 3-dimensional analogue of a disk;