I want to get a detailed explanation (i.e via special cases and illustrations) of Schlafli's differential formula for calculation of n-dimensional volume. My motivation is to understand a result of Gauss on volume of hyperbolic tetrahedron. First let's write Schlafli's differential formula:
$$ dV = -\frac12 \sum_{ij}l_{ij} d \alpha_{ij},$$ where $l$ is the length of the edge, and $\alpha$ is the dihedral angle of the edge. I want to try and understand it first in the 2-dimensional non-euclidean case - by examples on spherical and hyperbolic triangles. After this, i still want to get explanation for the 3-dimensional spherical and hyperbolic case (by examples on spherical and hyperbolic polyhedra). I ask this question since it was difficult to find elementary discussions of this formula.
Thanks for everyone who will help me. This is such a wonderful website for getting answers to you questions.