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Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

A Cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension). The condition for three general Cevians from the three ...

The circumcircle of the Cevian triangle DeltaA^'B^'C^' of a given triangle DeltaABC with respect to a point P. The following table summarizes a number of named Cevian circles ...

A Cevian point P is point with respect to which a set of Cevians of a triangle are taken. Connecting the endpoints of the Cevians through a point P gives the so-called Cevian ...

Vandeghen's (1965) name for the transformation taking points to their isotomic conjugates.

Given a point P and a triangle DeltaABC, the Cevian triangle DeltaA^'B^'C^' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A ...

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 ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...

Let A be a commutative ring, let C_r be an R-module for r=0, 1, 2, ..., and define a chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0. ...

Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and ...