Poincare (hyperbolic) geometry realized with macros.

This geometry can be realized on the southern hemisphere of a ball. You are viewing at it from the north pole. The green circle is the projection of the southern hemisphere, the boundary is the equator. This projection is called stereographical projection. It preserves angles.

Lines are circles on the ball, rectangular to the equator. These circles project to circles perpendicular to the boundary of the green circle. Circles are just circles on the ball. They project to circles, but with different midpoint.

Take care to use the macro for intersections. It will intersect two lines (circles in the projection), but choose the intersection in the green circle.