The hyperbolic polar sine is a function of an 
-dimensional simplex in hyperbolic space. It is analogous to
the polar sine of an 
-dimensional simplex in elliptic or spherical space. If the
edges between vertices 
and 
have length 
, the value of the hyperbolic polar sine of the 
-dimensional hyperbolic simplex 
in space with Gaussian curvature 
is given by
 |
The hyperbolic polar sine is used in the generalized law of sines for a hyperbolic simplex.
The limit of the hyperbolic polar sine of an 
-dimensional hyperbolic simplex as the curvature 
of the space approaches zero is 
, where 
is the content of the Euclidean simplex with the same edge
lengths.
