This is a visualization showing the Poincaré disk model of hyperbolic geometry. The entire geometry is located within the unit circle. Hyperbolic lines are actually arcs of a circle that intersect at right angles to the unit circle. Hyperbolic circles looks like Euclidean circles contained entirely within the unit circle, except the hyperbolic center is not in general the Euclidean center.

Notice how the same Euclidean length at the edge of the circle is much longer than near the center, this is due to the hyperbolic geometry, which has a very different distance function. See my accompanying blog post on Hyperbolic Geometry and Poincaré Embeddings for more details.

(NOTE: There are still a few kinks for some corner cases (near straight lines, circles near the edge) that don't quite draw the right thing due to the hacky numeric methods I used, but for the most part the lines and circles works as expected.)