A normal plane is any plane containing the normal vector of a surface at a particular point.
The normal plane also refers to the plane that is perpendicular to the tangent vector of a space curve; (this plane also contains the normal vector) see Frenet–Serret formulas.
YouTube Encyclopedic
-
1/3Views:192 92451 07481 872
-
What is a Plane? | Geometry | Don't Memorise
-
Class 12th – Definition of Plane | Three Dimensional Geometry | Tutorials Point
-
Equations of Planes: Vector & Component Forms | Multivariable Calculus
Transcription
Normal section
The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane.[1][2][3]
The curvature of the normal section is called the normal curvature.
If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures.
If the surface is saddle shaped the maxima of both sides are the principal curvatures.
The product of the principal curvatures is the Gaussian curvature of the surface (negative for saddle shaped surfaces).
The mean of the principal curvatures is the mean curvature of the surface; if (and only if) the mean curvature is zero, the surface is called a minimal surface.
See also
- Earth normal section
- Normal bundle
- Normal curvature
- Osculating plane
- Principal curvature
- Tangent plane (geometry)
References
- ^ Ruane, Irving Adler, with diagrams by Ruth Adler; introduction to the Dover edition by Peter (2012). A new look at geometry (Dover ed.). Mineola, N.Y.: Dover Publications. p. 273. ISBN 978-0486498515.
{{cite book}}: CS1 maint: multiple names: authors list (link) - ^ Irving Adler (2013-08-30). A New Look at Geometry. p. 273. ISBN 9780486320496. Retrieved 2016-04-01.
- ^ Alfred Gray (1997-12-29). Modern Differential Geometry of Curves and Surfaces with Mathematica, Second ... p. 365. ISBN 9780849371646. Retrieved 2016-04-01.
 | This differential geometry-related article is a stub. You can help Wikipedia by expanding it. |
This page was last edited on 26 January 2024, at 15:46