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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.

A geometry in which Archimedes' axiom does not hold.

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).

The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

Lachlan's term for a set of four points, no three of which are collinear.

The three-chord lemma states that in the figure above, l_1+l_2=2lcostheta.