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In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
In 2006, two mathematicians using Mathematica analyzed the function, and found variants where leaves, flowers or other insects became apparent. [3] See also.
Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable examples include plane curves , space curves , polyhedra , ordinary differential equations , partial differential equations (particularly numerical solutions, as in fluid dynamics or minimal surfaces such as soap films ...
regular 5-polytope 5-dimensional cross-polytope; 5-dimensional hypercube; 5-dimensional simplex; Five-dimensional space, 5-polytope and uniform 5-polytope. 5-simplex, Rectified 5-simplex, Truncated 5-simplex, Cantellated 5-simplex, Runcinated 5-simplex, Stericated 5-simplex; 5-demicube, Truncated 5-demicube, Cantellated 5-demicube, Runcinated 5 ...
For every scalar function of position and time λ(x, t), the potentials can be changed by a gauge transformation as ′ =, ′ = + without changing the electric and magnetic field. Two pairs of gauge transformed potentials ( φ , A ) and ( φ ′, A ′) are called gauge equivalent , and the freedom to select any pair of potentials in its gauge ...
Jacobi forms are a mixture of modular forms and elliptic functions. Examples of such functions are very classical - the Jacobi theta functions and the Fourier coefficients of Siegel modular forms of genus two - but it is a relatively recent observation that the Jacobi forms have an arithmetic theory very analogous to the usual theory of modular ...
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space.
An animation of Boy's surface. In geometry, Boy's surface is an immersion of the real projective plane in three-dimensional space.It was discovered in 1901 by the German mathematician Werner Boy, who had been tasked by his doctoral thesis advisor David Hilbert to prove that the projective plane could not be immersed in three-dimensional space.