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The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum ...

Given a factor a of a number n=ab, the cofactor of a is b=n/a. A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor M_(ij) defined ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the commutant M^' of an arbitrary subset M subset= L(H) is the ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

A conjugate matrix is a matrix A^_ obtained from a given matrix A by taking the complex conjugate of each element of A (Courant and Hilbert 1989, p. 9), i.e., ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...

The contrapedal curve, also called a normal pedal curve, is defined analogously to a usual pedal curve with "tangent" replaced by "normal." In particular, the contrapedal ...

Let x->y and u->v be two rules of a term rewriting system, and suppose these rules have no variables in common. If they do, rename the variables. If x_1 is a subterm of x (or ...

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...