>>11591372Think about the relationship between Earth and mars. We have lattitude and longitude lines on earth, right? We call them "lines," right? But lines go into space indefinitely. yet these "lines" never reach mars. Thus, spherical geometry.
Now think about lines on a hyperbola. Make sure they satisfy whatever algebraic/geometric/analytic property your prof told you about (I forgot it's been so long, lol. Cross-ratio?). Now imagine the hyperbola is some kind of object sitting in Euclidean 3-space. write the parametric equations for lines x, y and R as curves in Euclidean 3-space. Can you find an intersection point? If you did everything right, you shouldn't be able to.
>I don't understandAfter doing everything above, compare your work in Euclidean geometry to your notes in non-Euclidean geometry. You should be able to find a bunch of big equations/steps in your euclidean space that are analogous to much simpler stuff in non-Euclidean geometry. Now repeat the work in Euclidean 3-space for lines on a generalized hyperbola in Euclidean 4-space. Does your understanding of hyperbolic geometry make it any simpler?
