Parabolic Geodesic

Author

Eric W. Weisstein
February 12, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialGeometry/ParaboloidGeodesic.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ParaboloidGeodesic.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Parameters

paraboloid={(Sqrt[u ])Cos[v],(Sqrt[u ])Sin[v],u};

P

Total[((D[paraboloid,u])^2)]//Simplify

Q

Total[D[paraboloid,u,v]]//Simplify

R

Total[((D[paraboloid,v])^2)]//Simplify