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A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...

A general system of fourth-order curvilinear coordinates based on the cyclide in which Laplace's equation is separable (either simply separable or R-separable). Bôcher (1894) ...

If a complex function is analytic at all finite points of the complex plane C, then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112). Any ...

The Euler triangle of a triangle DeltaABC is the triangle DeltaE_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

Using the notation of Byerly (1959, pp. 252-253), Laplace's equation can be reduced to (1) where alpha = cint_c^lambda(dlambda)/(sqrt((lambda^2-b^2)(lambda^2-c^2))) (2) = ...

The second solution Q_l(x) to the Legendre differential equation. The Legendre functions of the second kind satisfy the same recurrence relation as the Legendre polynomials. ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...