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Every smooth manifold M has a tangent bundle TM, which consists of the tangent space TM_p at all points p in M. Since a tangent space TM_p is the set of all tangent vectors ...

Krall and Fink (1949) defined the Bessel polynomials as the function y_n(x) = sum_(k=0)^(n)((n+k)!)/((n-k)!k!)(x/2)^k (1) = sqrt(2/(pix))e^(1/x)K_(-n-1/2)(1/x), (2) where ...

There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

The placement of objects so that they touch in some specified manner, often inside a container with specified properties. For example, one could consider a sphere packing, ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Pre-Algebra

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...

The hyperbolic cosecant is defined as cschz=1/(sinhz)=2/(e^z-e^(-z)). (1) It is implemented in the Wolfram Language as Csch[z]. It is related to the hyperbolic cotangent ...