tangent

Also known as tangent line

AI overview

A tangent is a line or plane that touches a curve or surface at exactly one point without crossing through it. Tangents matter because they help mathematicians and scientists describe how curves and surfaces change direction at specific points, which is essential for understanding motion, slopes, and the behavior of shapes.

AI-generated from the Wikipedia summary — may contain errors.

Described at

Calculus I - Tangent Lines and Rates of Change

In this section we will introduce two problems that we will see time and again in this course : Rate of Change of a function and Tangent Lines to functions. Both of these problems will be used to introduce the concept of limits, although we won't formally give the definition or notation until the next section.

tutorial.math.lamar.edu →

At the second point shown (the point where the line isn’t a tangent line) we will sometimes call the line a secant line . Okay, now that we’ve gotten the definition of a tangent line out of the way let’s move on to the tangent line problem. That’s probably best done with an example.

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Wikidata facts

Image: Image Tangent-plane.svg

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Commons category: Tangency
described at URL: www.cuemath.com/calculus/tangent-line

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~19 min read

Article

19 sections

Contents

Etymology
History
Tangent line to a plane curve{{anchor|Line}}
Analytical approach
Intuitive description
More rigorous description
How the method can fail
Equations
Normal line to a curve
Angle between curves
Multiple tangents at a point
Tangent line to a space curve
Tangent circles
Tangent plane to a surface{{anchor|For surfaces|Surfaces|Plane}}
Higher-dimensional manifolds
See also
References
Sources
External links

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, 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 precisely, a straight line is tangent to the curve at a point if the line passes through the point on the curve and has slope , where f is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.