Secant line a circle in the Euclidean plane, a line joining two of them would be a 2-secant (or "bisecant") and a line passing through only one of them would be a 1-secant (or "unisecant"). A unisecant in this example need not be a tangent line to the circle. This terminology is often used in incidence geometry and discrete geometry. For instance, the Sylvester–Gallai theorem of incidence geometry states that if points of Euclidean geometry are not collinear then there must exist a 2-secant of them. And the original orchard-planting problem of discrete geometry asks for a bound on the number of
Affine geometry does not permute finite points with points at infinity, and affine transformation geometry is the study of geometrical properties through the action of the group of affine transformations. Affine geometry In mathematics, affine geometry is what remains of Euclidean geometry when not using (mathematicians often say "when forgetting") the metric notions of distance and angle. As the notion of "parallel lines" is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines. Therefore, Playfair's axiom ("given a line L and a point P not on L, there is