Normal (geometry) Normal (geometry) In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in two dimensions, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point. In three dimensions, a surface normal, or simply normal, to a surface at a point "P" is a vector that is perpendicular to the tangent plane to that surface at "P". The word "normal" is also used as an adjective: a line normal to a plane, the normal component
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