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A formal power series, sometimes simply called a "formal series" (Wilf 1994), of a field F is an infinite sequence {a_0,a_1,a_2,...} over F. Equivalently, it is a function ...

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

If there exists a one-to-one correspondence between two subgroups and subfields such that G(E(G^')) = G^' (1) E(G(E^')) = E^', (2) then E is said to have a Galois theory. A ...

The locus of a point P (or the envelope of a line) fixed in relation to a curve C which slides between fixed curves. For example, if C is a line segment and P a point on the ...

A root-finding algorithm which makes use of a third-order Taylor series f(x)=f(x_n)+f^'(x_n)(x-x_n)+1/2f^('')(x_n)(x-x_n)^2+.... (1) A root of f(x) satisfies f(x)=0, so 0 ...

Let a straight line AB be divided internally at C and externally at D in the same ratio, so that (AC)/(CB)=-(AD)/(DB). Then AB is said to be divided harmonically at C and D ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

The axioms formulated by Hausdorff (1919) for his concept of a topological space. These axioms describe the properties satisfied by subsets of elements x in a neighborhood ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...

A Hermitian form on a vector space V over the complex field C is a function f:V×V->C such that for all u,v,w in V and all a,b in R, 1. f(au+bv,w)=af(u,w)+bf(v,w). 2. ...