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The complementary subspace problem asks, in general, which closed subspaces of a Banach space are complemented (Johnson and Lindenstrauss 2001). Phillips (1940) proved that ...

A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...

_3F_2[n,-x,-y; x+n+1,y+n+1] =Gamma(x+n+1)Gamma(y+n+1)Gamma(1/2n+1)Gamma(x+y+1/2n+1) ×Gamma(n+1)Gamma(x+y+n+1)Gamma(x+1/2n+1)Gamma(y+1/2n+1), (1) where _3F_2(a,b,c;d,e;z) is a ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...

A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

The geometric mean of a sequence {a_i}_(i=1)^n is defined by G(a_1,...,a_n)=(product_(i=1)^na_i)^(1/n). (1) Thus, G(a_1,a_2) = sqrt(a_1a_2) (2) G(a_1,a_2,a_3) = ...

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...