tangent
Sign in to save220px|right|thumb|Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. 220px|right|thumb|Tangent plane to a sphere
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.
Article
19 sectionsContents
- 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
220px|right|thumb|Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. 220px|right|thumb|Tangent plane to a sphere
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.