In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a normal is an
object such as a
line,
ray
Ray may refer to:
Fish
* Ray (fish), any cartilaginous fish of the superorder Batoidea
* Ray (fish fin anatomy), a bony or horny spine on a fin
Science and mathematics
* Ray (geometry), half of a line proceeding from an initial point
* Ray (g ...
, or
vector that is
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
to a given object. For example, the normal line to a
plane curve at a given point is the (infinite) line perpendicular to the
tangent line
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More ...
to the curve at the point.
A normal vector may have length one (a
unit vector) or its length may represent the curvature of the object (a ''
curvature vector''); its
algebraic sign may indicate sides (interior or exterior).
In three dimensions, a surface normal, or simply normal, to a
surface at point
is a
vector perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
to the
tangent plane of the surface at P. The word "normal" is also used as an adjective: a
line ''normal'' to a