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The Kuratowski reduction theorem states that very nonplanar graph contains either the utility graph UG=K_(3,3) or the pentatope graph K_5 as a graph minor. The graphs K_(3,3) ...

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

A unique factorization domain, called UFD for short, is any integral domain in which every nonzero noninvertible element has a unique factorization, i.e., an essentially ...

The digraph intersection of two digraphs is the digraph whose vertex set (respectively, edge set) is the intersection of their vertex sets (respectively, edge sets). If n is ...

A continuous real function L(x,y) defined on the tangent bundle T(M) of an n-dimensional smooth manifold M is said to be a Finsler metric if 1. L(x,y) is differentiable at ...

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called hyperbolic if the matrix Z=[A B; B C] (2) ...

The Leonine triangle DeltaX_AX_BX_C (a term coined here for the first time), is the Cevian triangle of Kimberling center X_(598). It is the polar triangle of the Lemoine ...

The MacBeath triangle DeltaX_AX_BX_C (a term coined here for the first time), is the triangle whose vertices are the contact points of the MacBeath inconic with the reference ...

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...