Parallelism and Geodesy in Non-Euclidean Geometry

19/09/2007 - 14:49 von Narasimham | Report spam
Consider the double set of skewed straight line generators of a one-
sheet hyperboloid of revolution, a 2D surface in 3D. Which of the
following seven statements regarding geodesy/parallelism in non-
Euclidean geometry are true/ false?

1. They are geodesics in elliptic geometry.
2. They are geodesics in hyperbolic geometry.
3. They are geodesics in both elliptic/hyperbolic geometries.
4. They are a parallel to each other in elliptic geometry including
the axis of symmetry.
5. They are a parallel to each other in hyperbolic geometry including
the axis of symmetry.
6. They are a parallel to each other in elliptic geometry excluding
the axis of symmetry.
7. They are a parallel to each other in hyperbolic geometry excluding
the axis of symmetry.

Many TIA.

Regards,
Narasimham
 

Lesen sie die antworten

#1 Narasimham
20/09/2007 - 02:02 | Warnen spam
On Sep 19, 5:49 pm, Narasimham wrote:

Consider the double set of skewed straight line generators of a one-
sheet hyperboloid of revolution..



given e.g., in the first half of

http://mathworld.wolfram.com/Hyperboloid.html

Ähnliche fragen