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
Hyperbolic geometry of a circle of radius "r" is equal to: And the area of the enclosed disk is: Therefore, in hyperbolic geometry the ratio of a circle's circumference to its radius is always strictly greater than formula_7, though it can be made arbitrarily close by selecting a small enough circle. If the Gaussian curvature of the plane is −1 then the geodesic curvature of a circle of radius "r" is: formula_8 In hyperbolic geometry, there is no line that remains equidistant from another. Instead, the points that all have the same orthogonal distance from a given line lie on a curve