Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
- Additional Readings
A term generically synonymous with perpendicular, which often refers specifically to a line that goes through a point P of a curve C and is perpendicular to the tangent to C at P. If a plane curve C has equation y = f(x), in rectangular coordinates the normal (line) to C at P(x0,y0) has slope −1/f′(x0), provided f′(x0) ≠ 0. The expression f′(x0) denotes the derivative of f(x), evaluated for x = x0, and so the normal has equation y − y0 = [−1/f′(x0)] (x − x0). If curve C is not a plane curve, all normal lines of C at point P on C lie in a plane, the normal plane of C at P. For other uses of normal (for example, normal form of equation of a line or a plane) See also: Analytic geometry .
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