- Pi
- Asymptotic curve
- Asymptote
- Asymptotic analysis
- Big O notation
- List of curves topics
- Normal distribution
- Receiver operating characteristic
- Logistic function
- Witch of Agnesi
- Stokes phenomenon
- Asymptotic curve - Wikipedia
- Asymptote - Wikipedia
- Asymptotic Curve -- from Wolfram MathWorld
- Asymptotic Curve - GeeksforGeeks
- Asymptote - Definition, Rules, Equations, Examples, and Diagrams
- Asymptotic curve Definition & Meaning - Merriam-Webster
- How to find asymptotes: simple illustrated guide and examples
- Finding the Asymptotic Curves of a Given Surface
- Asymptote -- from Wolfram MathWorld
- Asymptote Formula - GeeksforGeeks
Asymptotic curve GudangMovies21 Rebahinxxi LK21
In the differential geometry of surfaces, an asymptotic curve is a curve always tangent to an asymptotic direction of the surface (where they exist). It is sometimes called an asymptotic line, although it need not be a line.
Definitions
There are several equivalent definitions for asymptotic directions, or equivalently, asymptotic curves.
The asymptotic directions are the same as the asymptotes of the hyperbola of the Dupin indicatrix through a hyperbolic point, or the unique asymptote through a parabolic point.
An asymptotic direction is a direction along which the normal curvature is zero: take the plane spanned by the direction and the surface's normal at that point. The curve of intersection of the plane and the surface has zero curvature at that point.
An asymptotic curve is a curve such that, at each point, the plane tangent to the surface is an osculating plane of the curve.
Properties
Asymptotic directions can only occur when the Gaussian curvature is negative (or zero).
There are two asymptotic directions through every point with negative Gaussian curvature, bisected by the principal directions. There is one or infinitely many asymptotic directions through every point with zero Gaussian curvature.
If the surface is minimal and not flat, then the asymptotic directions are orthogonal to one another (and 45 degrees with the two principal directions).
For a developable surface, the asymptotic lines are the generatrices, and them only.
If a straight line is included in a surface, then it is an asymptotic curve of the surface.
Related notions
A related notion is a curvature line, which is a curve always tangent to a principal direction.
References
Weisstein, Eric W. "Asymptotic Curve". MathWorld.
Lines of Curvature, Geodesic Torsion, Asymptotic Lines
"Asymptotic line of a surface" at Encyclopédie des Formes Mathématiques Remarquables (in French)
Kata Kunci Pencarian:
Asymptotic Curve | The Paddison Program for Rheumatoid Arthritis
Asymptotic Curve -- from Wolfram MathWorld
Asymptotic Curve -- from Wolfram MathWorld
Asymptotic Curve -- from Wolfram MathWorld
Asymptotic Curve -- from Wolfram MathWorld
Asymptotic theory
Asymptotic Curve - GeeksforGeeks
Asymptotic Notation | Engati
Asymptotic Behavior - Statistics How To
What is an asymptotic curve? - The Handy Math Answer Book
(1) Dynamics of the observed asymptotic curve in the numerical analysis ...
(1) Dynamics of the observed asymptotic curve in the numerical analysis ...
asymptotic curve
Daftar Isi
Asymptotic curve - Wikipedia
In the differential geometry of surfaces, an asymptotic curve is a curve always tangent to an asymptotic direction of the surface (where they exist). It is sometimes called an asymptotic …
Asymptote - Wikipedia
In analytic geometry, an asymptote (/ ˈ æ s ɪ m p t oʊ t /) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends …
Asymptotic Curve -- from Wolfram MathWorld
4 days ago · Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of x.
Asymptotic Curve - GeeksforGeeks
Jul 26, 2024 · An asymptotic curve is a line that a given curve approaches but never actually meets as it extends toward infinity. In simpler terms, as the distance between the two curves …
Asymptote - Definition, Rules, Equations, Examples, and Diagrams
Aug 28, 2023 · An asymptote is a straight line or a curve that approaches a given curve as it heads toward infinity but never meets the curve. Such a pair of curves is called an asymptotic …
Asymptotic curve Definition & Meaning - Merriam-Webster
The meaning of ASYMPTOTIC CURVE is a curve on a surface whose osculating plane at each point coincides with the tangent plane to the surface at that point.
How to find asymptotes: simple illustrated guide and examples
Nov 25, 2020 · Explains how to find asymptotes, with illustrations and examples for all 4 types of asymptotes: vertical, horizontal, skewed and asymptotic curve.
Finding the Asymptotic Curves of a Given Surface
Now you can use Corollary 18.6. from Chapter 18 of A.Gray, E.Abbena and S.Salamon "Modern Differential Geometry of Curves and Surfaces with Mathematica" stating that "A straight line …
Asymptote -- from Wolfram MathWorld
4 days ago · An asymptote is a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram. The plot above shows 1/x, which has a vertical asymptote at …
Asymptote Formula - GeeksforGeeks
Jun 18, 2024 · In geometry, an asymptote is a straight line that approaches a curve on the graph and tends to meet the curve at infinity. An asymptote is a line that a graph of a function …