Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Analytic geometry
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==Spherical and nonlinear planes and their tangents== Tangent is the linear approximation of a spherical or other curved or twisted line of a function. ===Tangent lines and planes=== {{main|Tangent}} In [[geometry]], the '''tangent line''' (or simply '''tangent''') to a plane [[curve]] at a given [[Point (geometry)|point]] is the [[straight line]] that "just touches" the curve at that point. Informally, it is a line through a pair of [[infinitesimal|infinitely close]] points on the curve. More precisely, a straight line is said to be a tangent of a curve {{nowrap|1=''y'' = ''f''(''x'')}} at a point {{nowrap|1=''x'' = ''c''}} on the curve if the line passes through the point {{nowrap|(''c'', ''f''(''c''))}} on the curve and has slope {{nowrap|''f''{{'}}(''c'')}} where ''f''{{'}} is the [[derivative]] of ''f''. A similar definition applies to [[space curve]]s and curves in ''n''-dimensional [[Euclidean space]]. As it passes through the point where the tangent line and the curve meet, called the '''point of tangency''', the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. Similarly, the '''tangent plane''' to a [[Surface (mathematics)|surface]] at a given point is the [[Plane (mathematics)|plane]] that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in [[differential geometry]] and has been extensively generalized; see [[Tangent space]].
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)