Image:UHS geodesics.png

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Geodesics in upper half space model of three-dimensional hyperbolic space H³. The metric is

$ds^2 = \frac{dx^2+dy^2+dz^2}{x^2}, \; \; 0 < x < \infty, \; \; -infty < y,z < \infty$

Some typical geodesics through one point are shown in black. They appear as semicircular arcs in the upper half space chart. The magenta plane represents the "sphere at infinity", which is located at $x = 0$ in this chart.

This is a png image converted by eog from a jpg image created by User:Hillman using Maple.

I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
Subject to disclaimers.

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(del) (cur) 16:25, 31 May 2006 . . Drat (Talk | contribs) . . 400×400 (2,208 bytes) (Cleaned up and colours reduced (why do people create PNGs from Jpegs?), and optimised with OptiPNG.)
(del) (rev) 23:37, 4 May 2006 . . Hillman (Talk | contribs) . . 400×400 (37,198 bytes) (Geodesics in upper half space model of three-dimensional hyperbolic space '''H'''<sup>3</sup>. The metric is :<math> ds^2 = \frac{dx^2+dy^2+dz^2}{x^2}, \; \; 0 < x < \infty, \; \; -infty < y,z < \infty </math> Some typical geodesics through one point are)