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Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

The BCI triangle DeltaA^'B^'C^' of a triangle DeltaABC with incenter I is defined by letting A^' be the center of the incircle of DeltaBCI, and similarly defining B^' and ...

Bipolar coordinates are a two-dimensional system of coordinates. There are two commonly defined types of bipolar coordinates, the first of which is defined by x = ...

A set of curvilinear coordinates defined by x = (asinhv)/(coshv-cosu) (1) y = (asinu)/(coshv-cosu) (2) z = z, (3) where u in [0,2pi), v in (-infty,infty), and z in ...

The midpoint of the first and second Brocard points Omega and Omega^'. It has equivalent triangle center functions alpha = a(b^2+c^2) (1) alpha = sin(A+omega), (2) where ...

Consider a quadratic equation x^2-sx+p=0 where s and p denote signed lengths. The circle which has the points A=(0,1) and B=(s,p) as a diameter is then called the Carlyle ...

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 circular pattern obtained by superposing parallel equally spaced lines on a set of concentric circles of increasing radii, then coloring the regions in chessboard fashion. ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

Given two curves C_1 and C_2 and a fixed point O, let a line from O cut C_1 at Q and C_2 at R. Then the locus of a point P such that OP=QR is the cissoid. The word cissoid ...