Definition of Tangent Plane
A tangent plane to a surface at a given point is a flat plane that just touches the surface at that point. It is defined such that at the point of tangency, the plane and the surface share the same tangent line, representing the direction of the surface’s slope at that point. This tangent plane serves as an approximation of the surface’s behavior in the vicinity of the point of tangency, allowing for the study of local properties such as gradient, normal vector, and curvature.
Tangent Plane to a Surface
A tangent plane is a flat surface that touches a curve or surface at a single point, sharing the same slope or direction at that point, facilitating local approximation in calculus. This article discusses tangent planes, which are flat surfaces that touch curves or surfaces at specific points. It explains their definition, how to calculate them, and their geometric interpretation. It also explores their applications in various fields like engineering, physics, and computer graphics.
Table of Content
- Definition of Tangent Plane
- How to Find the Tangent Plane to a Surface
- Tangent Plane Equation
- Geometric Interpretation of the Tangent Plane
- Applications of Tangent Plane to a Surface
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