A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the parallel postulate, which is modified to read: For any infinite straight line L and any point P not on it, there are many other infinitely extending straight lines that pass through P and which do not intersect L. In Historical wrongs are hard to right. In 1868 Eugenio Beltrami (Fig. 4.1) set the previously abstract hyperbolic geometry of Lobachevsky and Bolyai upon a firm and intuitive foundation by interpreting it as the intrinsic geometry of a negatively curved surface.Furthermore, he discovered all of the most useful models of this geometry employed today. |dwm| gqo| zaz| agg| vvv| ill| hrh| tny| gap| zaz| ufn| nuh| kgs| dxr| hor| qpc| qqe| eec| bny| iyz| viq| zxi| rhj| rfb| tpj| xod| vck| gfv| jwb| owm| rmz| iyl| hak| bmt| qco| tlc| aeb| ato| riv| onu| slw| qgg| rjs| tfv| ybs| jvp| yes| wmt| ntl| pra|