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Given a matrix equation Ax=b, the normal equation is that which minimizes the sum of the square differences between the left and right sides: A^(T)Ax=A^(T)b. It is called a ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider a ...

A Thue equation is a Diophantine equation of the form A_nx^n+A_(n-1)x^(n-1)y+A_(n-2)x^(n-2)y^2+...+A_0y^n=M in terms of an irreducible polynomial of degree n>=3 having ...

The functional equation phi(f(x))=sphi(x), with s!=0,1.

The Diophantine equation x^n+y^n=z^n. The assertion that this equation has no nontrivial solutions for n>2 has a long and fascinating history and is known as Fermat's last ...

The partial differential equation (Cole and Cook 1986, p. 34; Zwillinger 1997, p. 134).

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

dtau^2=-eta_(alphabeta)dxi^alphadxi^beta, or (d^2xi^alpha)/(dtau^2)=0.