Hi there!(adsbygoogle = window.adsbygoogle || []).push({});

I´ve come upon the following problem: I want to determine the set of all lines of the following surface:

[tex]x_1^2+x_2^2-x_3^2=1[/tex]

Here´s my idea: if one could determine one line parametrised by an angle and a radius, one could define the whole surface as rotation of this line over the x_3-axis. One can write every point of the surface as [tex]rcos\phi,rsin\phi,\sqrt{r^2-1}[/tex] where r is supposed to be the vector of any circle, got by a slice, parallel to the x_1x_2-plane

We then go to the otherside of the x_1x_2-plane, to get (by symmetry) onother circle with radius of the same length. If we define another point on it, it will be of the form [tex]rcos\psi,rsin\psi,-\sqrt{r^2-1}[/tex].

I claim (by intuition) that the phase difference between the angles will be constant for every line, but I cannot prove it :(

Can someone please help me, or give me a hint?

Thanks a lot in advance, Marin

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Parametrising a surface

Loading...

Similar Threads - Parametrising surface | Date |
---|---|

Intersection of line and surface | May 29, 2015 |

Quadratic surfaces + principle axes | Sep 28, 2011 |

Equation of a Surface relative to a basis | Apr 1, 2011 |

Checking for a point inside a region of a spherical surface | Jun 23, 2008 |

**Physics Forums - The Fusion of Science and Community**