tangent plane
Barely kissing surface
A tangent plane is a flat surface that touches a curved surface at exactly one point, extending in the direction the curve is heading at that moment.
In calculus, it represents the best linear approximation to a surface at a given point—the three-dimensional analogue of a tangent line to a curve: The tangent plane to a sphere touches it at precisely one point.
Approximating nonlinear with linear
- partial derivativeDifferentiation fixing other variables
- gradientRate of change across space
- multivariableHaving several independent variables
- differentiableHaving a derivative
approximation · critical point · saddle point · extrema · constraint · optimization · chain rule · continuity
Outermost boundary layer
- perpendicularAt right angles
- curvatureDeviation from flatness
- affineRelative by marriage
- contact pointMeeting spot between surfaces
local approximation · flatness · orientation · projection · intersection · parametrization · manifold · secant
linearization
Approximating nonlinear with linear
- partial derivativeDifferentiation fixing other variables
- gradientRate of change across space
- multivariableHaving several independent variables
differentiable · approximation · critical point · saddle point · extrema · constraint · optimization · chain rule · continuity
surface
Outermost boundary layer
- perpendicularAt right angles
- curvatureDeviation from flatness
- affineRelative by marriage
contact point · local approximation · flatness · orientation · projection · intersection · parametrization · manifold · secant · slope