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The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

Let x:U->R^3 be a regular patch, where U is an open subset of R^2. Then (partiale)/(partialv)-(partialf)/(partialu) = eGamma_(12)^1+f(Gamma_(12)^2-Gamma_(11)^1)-gGamma_(11)^2 ...

Let p_n be the nth prime, then the primorial (which is the analog of the usual factorial for prime numbers) is defined by p_n#=product_(k=1)^np_k. (1) The values of p_n# for ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

The wave equation in prolate spheroidal coordinates is del ...

Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros sigma+it with 0<t<=T is asymptotically given by ...