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For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle : The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an ...
Parabolic cylinder () function appears naturally in the Schrödinger equation for the one-dimensional quantum harmonic oscillator (a quantum particle in the oscillator potential), [+] = (), where is the reduced Planck constant, is the mass of the particle, is the coordinate of the particle, is the frequency of the oscillator, is the energy, and () is the particle's wave-function.
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length. For cylinders with diameters on the same order of magnitude as the spheres, such packings result in what are called columnar structures .
Codes for electromagnetic scattering by cylinders – this article list codes for electromagnetic scattering by a cylinder. Majority of existing codes for calculation of electromagnetic scattering by a single cylinder are based on Mie theory , which is an analytical solution of Maxwell's equations in terms of infinite series.
Then the formula for the volume will be: If the function is of the y coordinate and the axis of rotation is the x-axis then the formula becomes: If the function is rotating around the line x = h then the formula becomes: [1]
As can be seen, the area of the circle defined by the intersection with the sphere of a horizontal plane located at any height equals the area of the intersection of that plane with the part of the cylinder that is "outside" of the cone; thus, applying Cavalieri's principle, it could be said that the volume of the half sphere equals the volume ...
The new proofs involve using the Laplace transform of a carefully chosen modular function to construct a radially symmetric function f such that f and its Fourier transform f̂ both equal 1 at the origin, and both vanish at all other points of the optimal lattice, with f negative outside the central sphere of the packing and f̂ positive.
The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV. The fluid displaced has a weight W = mg, where g is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as W = ρVg.