Hyperbolic sector

A hyperbolic sector is a region in the plane that is defined by certain properties of hyperbolic geometry, which is a non-Euclidean geometry that arises when the parallel postulate of Euclidean geometry is replaced with an alternative. In hyperbolic geometry, the sum of the angles of a triangle is less than 180 degrees, and there are infinitely many lines parallel to a given line through a point not on that line.