The schlafli differential formula based on edge lenghts of simplices in the hiperpolic and spherical spaces

Within this thesis, dominant formulas depending on only edge lengths of a spherical or hyperbolical tetrahedron which are different from Lobachevski and Schlafli differential formula are obtained. Since these formulas are similar to Schlafli differential formula, they are named as Schlafli differential formula depending on edge lengths. Forms of these formulas for particular spherical and hyperbolical tetrahedra are derived. Calculations with both Lobachevski formula and Schlafli differential formula depending on edge lengths were carried out for the ideal regular hyperbolical tetrahedron in order to make comparison also. So the formulas are validated numerically. The relations of spherical and hyperbolical simplices with Feynman integrals were given and the application of Schlafli differential formula depending on edge lengths on calculation of Feynman integrals was considered.