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An equichordal point is a point p for which all the chords of a curve C passing through p are of the same length. In other words, p is an equichordal point if, for every ...

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

A number which is simultaneously pentagonal and hexagonal. Let P_n denote the nth pentagonal number and H_m the mth hexagonal number, then a number which is both pentagonal ...

Let H_n denote the nth hexagonal number and S_m the mth square number, then a number which is both hexagonal and square satisfies the equation H_n=S_m, or n(2n-1)=m^2. (1) ...

The Hofstadter ellipses are a family of triangle ellipses introduced by P. Moses in February 2005. The Hofstadter ellipse E(r) for parameter 0<r<1 is defined by the trilinear ...

Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

The Jackson-Slater identity is the q-series identity of Rogers-Ramanujan-type given by sum_(k=0)^(infty)(q^(2k^2))/((q)_(2k)) = ...