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The solid angle of a sphere measured from any point in its interior is 4 π sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. Solid angles can also be measured in square degrees (1 sr = (180/ π) 2 square degrees), in square arc-minutes and square arc-seconds, or in fractions of ...
1 m 2 /m 2. square degrees. 1802 / π2 deg2. ≈ 3 282.8 deg 2. The steradian (symbol: sr) or square radian[1][2] is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in steradians, projected onto a sphere ...
The omega constant is a mathematical constant defined as the unique real number that satisfies the equation. It is the value of W(1), where W is Lambert's W function. The name is derived from the alternate name for Lambert's W function, the omega function. The numerical value of Ω is given by.
The lambda cube. Direction of each arrow is direction of inclusion. In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt [1] to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus.
In additive number theory, Fermat 's theorem on sums of two squares states that an odd prime p can be expressed as: with x and y integers, if and only if. The prime numbers for which this is true are called Pythagorean primes. For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of ...
Reduced specific heat for KCl, TiO2, and graphite, compared with the Debye theory based on elastic measurements (solid lines). [1]In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 to estimate phonon contribution to the specific heat (heat capacity) in a solid. [2]
Hypercube graph. In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n -dimensional hypercube. For instance, the cube graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Qn has 2n vertices, 2n – 1n edges, and is a regular graph with n edges touching each vertex.
3 and each rational prime congruent to 1 mod 3 are equal to the norm x 2 − xy + y 2 of an Eisenstein integer x + ωy. Thus, such a prime may be factored as (x + ωy)(x + ω 2 y), and these factors are Eisenstein primes: they are precisely the Eisenstein integers whose norm is a rational prime.