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In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point. A normal vector of length one is called a unit normal vector.
The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane. [1] [2] [3] The curvature of the normal section is called the normal curvature. If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures.
In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain.An affine variety X (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain.
Normal order of an arithmetic function, a type of asymptotic behavior useful in number theory; Normal polytopes, in polyhedral geometry and computational commutative algebra; Normal ring, a reduced ring whose localizations at prime ideals are integrally closed domains; Normal scheme, a scheme whose local rings are normal domains; Normal ...
The normal line at a point of a surface is the unique line passing through the point and perpendicular to the tangent plane; the normal vector is a vector which is parallel to the normal. For other differential invariants of surfaces, in the neighborhood of a point, see Differential geometry of surfaces.
In terms of the vector space, the seminorm defines a topology on the space, and this is a Hausdorff topology precisely when the seminorm can distinguish between distinct vectors, which is again equivalent to the seminorm being a norm. The topology thus defined (by either a norm or a seminorm) can be understood either in terms of sequences or ...
Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.
A normal plane may refer to The plane perpendicular to the tangent vector of a space curve; see Frenet–Serret formulas. One of the planes containing the normal vector of a surface; see Normal plane (geometry). A term involving gears; see list of gear nomenclature.