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Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy |l_1 m_1 n_1; l_2 m_2 n_2; l_3 m_3 ...

A chord which is a normal at each end. A centrosymmetric set K subset R^d has d double normals through the center (Croft et al. 1991). For a curve of constant width, all ...

Any two ranges {ABC...} and {A^'B^'C^'...} which are situated on the same or different lines are said to be homographic when the cross ratio of any four points on one range ...

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

The isotomic transform of a geometric object is the object obtained by collectively taking the isotomic conjugates of all its points.

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

AW, AB, and AY in the above figure are in a harmonic range.

The maximal number of regions into which n lines divide a plane are N(n)=1/2(n^2+n+2) which, for n=1, 2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124), the same maximal ...

Any geometric correlation which transforms one range into a projectively related pencil (or vice versa).