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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 a heptagonal number H_n and square number S_m. Such numbers exist when 1/2n(5n-3)=m^2. (1) Completing the square and rearranging gives ...

A number which is simultaneously a heptagonal number H_n and triangular number T_m. Such numbers exist when 1/2n(5n-3)=1/2m(m+1). (1) Completing the square and rearranging ...

It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

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 ...