An asymptotic direction at a point of a regular surface is a direction in which the normal curvature of vanishes.

1. There are no asymptotic directions at an elliptic
point.

2. There are exactly two asymptotic directions at a hyperbolic
point.

3. There is exactly one asymptotic direction at a
parabolic point.

4. Every direction is asymptotic at a planar point.

## See also

Asymptotic Curve
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## References

Gray, A. *Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed.* Boca
Raton, FL: CRC Press, pp. 364 and 418, 1997.## Referenced on Wolfram|Alpha

Asymptotic Direction
## Cite this as:

Weisstein, Eric W. "Asymptotic Direction."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AsymptoticDirection.html

## Subject classifications