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Аннотация:A direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of (N - 1)-dimensional simplices in non-Euclidean geometry of constant curvature. In particular, the four-point function in four dimensions is proportional to the volume of a three-dimensional spherical (or hyperbolic);tetrahedron;which can be calculated by splitting into birectangular ones. It is also shown that the known formula of reduction of the N-point function in (N- I) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones. (C) 1998 American Institute of Physics.