# Does hyperbolic geometry actually take place on a hyperboloid?

Spherical geometry can be very easily seen in action on a sphere: if I drew on a ball, I would find triangles with sums of angles greater than 180 degrees, and parallel lines that intersect. If I were to draw on one of these

would I get the properties of hyperbolic geometry such as 5 squares meeting at a corner?

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Commented Oct 19, 2022 at 16:11
• Your question is quite vague. For instance, you have not said what geometry you are using on that hyperboloid. The meaning and relevance of "drawing" on the hyperboloid is also quite unclear. Commented Oct 19, 2022 at 18:27
• @LeeMosher I don’t know what you mean by “you have not said what geometry you are using”. By drawing I mean literally to draw: if I took a sharpie and scribbled on a plastic ball, I could construct a triangle with 3 90 degree angles. If I got my hands on a hyperboloid in real life, and i started scribbling, would I get things like diverging parallel lines and 5 right angled pentagons? Commented Oct 19, 2022 at 20:06
• If that's what you mean then no, you would not get a property of hyperbolic geometry such as five squares meeting at a corner, because drawing in that fashion is not consistent with the hyperboloid model of the hyperbolic plane. Commented Oct 20, 2022 at 0:32