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The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...

The secant numbers S_k, also called the zig numbers or the Euler numbers E_n^*=|E_(2n)| numbers than can be defined either in terms of a generating function given as the ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

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 ...

Given a reference triangle DeltaABC and a point P, the triple (x,y,z), with x=PA, y=PB and z=PC representing the distances from P to the vertices of the reference triangle, ...

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) ...

A number given by the generating function (2t)/(e^t+1)=sum_(n=1)^inftyG_n(t^n)/(n!). (1) It satisfies G_1=1, G_3=G_5=G_7=...=0, and even coefficients are given by G_(2n) = ...

A topologically invariant property of a surface defined as the largest number of nonintersecting simple closed curves that can be drawn on the surface without separating it. ...

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...