2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190769A 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-1) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones.47 pages, including 42 pages of the text (in plain Latex) and 5 pages with the figures (in a separate Latex file, requires axodraw.sty) a note and three references added, minor problem with notation fixedHigh Energy Physics - TheoryHigh Energy Physics - Phenomenologytext