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
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