Method of normals
Encyclopedia
In calculus
, the method of normals was a technique invented by Descartes for finding normal and tangent
lines to curves
. It represented one of the earliest methods for constructing tangents to curves. The method hinges on the observation that the radius of a circle is always normal to the circle itself. With this in mind Descartes would construct a circle that was tangent to a given curve. He could then use the radius at the point of intersection to find the slope of a normal line, and from this one can easily find the slope of a tangent line.
This was discovered about the same time as Fermat's method of adequality
. While Fermat's method had more in common with the infinitesimal techniques that were to be used later, Descartes method was more influential in the early history of calculus.
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
, the method of normals was a technique invented by Descartes for finding normal and tangent
Tangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...
lines to curves
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
. It represented one of the earliest methods for constructing tangents to curves. The method hinges on the observation that the radius of a circle is always normal to the circle itself. With this in mind Descartes would construct a circle that was tangent to a given curve. He could then use the radius at the point of intersection to find the slope of a normal line, and from this one can easily find the slope of a tangent line.
This was discovered about the same time as Fermat's method of adequality
Adequality
In the history of infinitesimal calculus, adequality is a technique developed by Pierre de Fermat. Fermat said he borrowed the term from Diophantus. Adequality was a technique first used to find maxima for functions and then adapted to find tangent lines to curves...
. While Fermat's method had more in common with the infinitesimal techniques that were to be used later, Descartes method was more influential in the early history of calculus.