What is the geometrical meaning of the common value in the law of sines, $\frac{\sin A}{\sinh a} = \frac{\sin B}{\sinh b} = \frac{\sin C}{\sinh c}$ in hyperbolic geometry? I know the meaning of this value only in Euclidean and spherical geometry.

EDIT, Will Jagy. The OP is looking for some fourth fairly natural real number that can be calculated from a triangle, that gives the same answer as the common value in the Law of Sines. The original question is at http://math.stackexchange.com/questions/69345/the-law-of-sines-in-hyperbolic-geometry

What is the geometrical meaning of the common value in the law of sines, $\frac{\sin A}{\sinh a} = \frac{\sin B}{\sinh b} = \frac{\sin C}{\sinh c}$ in hyperbolic geometry? I know the meaning of this value only in Euclidean and spherical geometry.

EDIT, Will Jagy. The OP is looking for some fourth fairly natural real number that can be calculated from a triangle, that gives the same answer as the common value in the Law of Sines. The original question is at https://math.stackexchange.com/questions/69345/the-law-of-sines-in-hyperbolic-geometry

What is the geometrical meaning of the constant $k$ in the law of sines, $\frac{\sin A}{\sinh a} = \frac{\sin B}{\sinh b} = \frac{\sin C}{\sinh c}=k$ in hyperbolic geometry? I know the meaning of the constant only in Euclidean and spherical geometry.

What is the geometrical meaning of the common value in the law of sines, $\frac{\sin A}{\sinh a} = \frac{\sin B}{\sinh b} = \frac{\sin C}{\sinh c}$ in hyperbolic geometry? I know the meaning of this value only in Euclidean and spherical geometry.

EDIT, Will Jagy. The OP is looking for some fourth fairly natural real number that can be calculated from a triangle, that gives the same answer as the common value in the Law of Sines. The original question is at http://math.stackexchange.com/questions/69345/the-law-of-sines-in-hyperbolic-geometry