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A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that ...
In mathematics, the theory of finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely many spheres has only been investigated in detail in recent decades, with much of the groundwork being laid by László Fejes Tóth .
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Graph of = /. Gabriel's horn is formed by taking the graph of =, with the domain and rotating it in three dimensions about the x axis. The discovery was made using Cavalieri's principle before the invention of calculus, but today, calculus can be used to calculate the volume and surface area of the horn between x = 1 and x = a, where a > 1. [6]
For example, to calculate the dynamics of a billiard ball being struck, one can approximate the force of the impact by a Dirac delta. In doing so, one not only simplifies the equations, but one also is able to calculate the motion of the ball, by only considering the total impulse of the collision, without a detailed model of all of the elastic ...
The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite. Likewise, the one-dimensional Hausdorff measure of a simple curve in R n {\displaystyle \mathbb {R} ^{n}} is equal to the length of the curve, and the two-dimensional Hausdorff measure of a Lebesgue-measurable subset ...
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. [1] In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals , using the divergence theorem .