Question

Which of the following are characteristics of hyperbolic geometry? Check all that apply. A. When represented on a Poincaré Disk, a line is an arc that has endpoints. B. Triangles have more than 180 degrees. C. It can be represented by a Poincaré Disk. D. There is an infinite number of lines parallel to a given line through a given point.

Answer 1

A. When represented on a Poincaré Disk, a line is an arc that has endpoints.

Answer 2

The hyperbolic geometry is a non-Euclidean geometry. Here we assume all the postulates of Euclid, except the fifth one. We take the negation of the fifth one.

So, the following are the characteristics of hyperbolic geometry

A. When represented on a Poincaré Disk, a line is an arc that has endpoints.

C. It can be represented by a Poincaré Disk.

D. There is an infinite number of lines parallel to a given line through a given point.

Note:

B. is false as triangles have less than 180 degrees.