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A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

The Markov numbers m are the union of the solutions (x,y,z) to the Markov equation x^2+y^2+z^2=3xyz, (1) and are related to Lagrange numbers L_n by L_n=sqrt(9-4/(m^2)). (2) ...

An algorithm similar to Neville's algorithm for constructing the Lagrange interpolating polynomial. Let f(x|x_0,x_1,...,x_k) be the unique polynomial of kth polynomial order ...

An identity in calculus of variations discovered in 1868 by Beltrami. The Euler-Lagrange differential equation is (partialf)/(partialy)-d/(dx)((partialf)/(partialy_x))=0. (1) ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

A theorem due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it ...

The end of the last gap in the Lagrange spectrum, given by F=(2221564096+283748sqrt(462))/(491993569)=4.5278295661... (OEIS A118472). Real numbers greater than F are members ...

Let l(x) be an nth degree polynomial with zeros at x_1, ..., x_n. Then the fundamental Hermite interpolating polynomials of the first and second kinds are defined by ...

Consider the Lagrange interpolating polynomial f(x)=b_0+(x-1)(b_1+(x-2)(b_3+(x-3)+...)) (1) through the points (n,p_n), where p_n is the nth prime. For the first few points, ...

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...