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The bifoliate is the quartic curve given by the Cartesian equation x^4+y^4=2axy^2 (1) and the polar equation r=(8costhetasin^2theta)/(3+cos(4theta))a (2) for theta in [0,pi]. ...

The bifolium is a folium with b=0. The bifolium is a quartic curve and is given by the implicit equation is (x^2+y^2)^2=4axy^2 (1) and the polar equation ...

The symbol O(x), pronounced "big-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n is ...

The bigyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(79). The unit bigyrate diminished rhombicosidodecahedron has volume ...

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") ...

A two-sided (doubly infinite) Z-Transform, Z^((2))[{a_n}_(n=-infty)^infty](z)=sum_(n=-infty)^infty(a_n)/(z^n) (Zwillinger 1996; Krantz 1999, p. 214). The bilateral transform ...

A bilinear form on a real vector space is a function b:V×V->R that satisfies the following axioms for any scalar alpha and any choice of vectors v,w,v_1,v_2,w_1, and w_2. 1. ...

A Bill picture is a sequence of nested regular polygons in which subsequent polygons are each rotated so that they begin one vertex further. The term was coined by Trott ...

In the American system, one billion equals 10^9=1000000000. In the French and German systems, one billion equals 10^(12). In recent years, the "American" system has become ...