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If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

The Fuhrmann triangle of a reference triangle DeltaABC is the triangle DeltaF_CF_BF_A formed by reflecting the mid-arc points arcM_A, arcM_B, arcM_C about the lines AB, AC, ...

A prime p for which 1/p has a maximal period decimal expansion of p-1 digits. Full reptend primes are sometimes also called long primes (Conway and Guy 1996, pp. 157-163 and ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

The fundamental theorem(s) of calculus relate derivatives and integrals with one another. These relationships are both important theoretical achievements and pactical tools ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...