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
Algebraic geometry points of algebraic geometry. The fact that the field of the real numbers is an ordered field cannot be ignored in such a study. For example, the curve of equation formula_8 is a circle if formula_9, but does not have any real point if formula_10. It follows that real algebraic geometry is not only the study of the real algebraic varieties, but has been generalized to the study of the "semi-algebraic sets", which are the solutions of systems of polynomial equations and polynomial inequalities. For example, a branch of the hyperbola of equation formula_11 is not an algebraic variety, but