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
Constructions in hyperbolic geometry Constructions in hyperbolic geometry Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the Parallel postulate, is changed. The fifth axiom of hyperbolic geometry says that given a line "L" and a point "P" not on that line, there are at least two lines passing through "P" that are parallel to "L". As in Euclidean geometry, where ancient Greek mathematicians used a compass and idealized ruler for constructions of lengths, angles, and other geometric figures, constructions can also be made in hyperbolic geometry. There are a couple of models