  We compute the metric associated to noncommutative spaces described by a
tensor product of spectral triples. Well known results of the two-sheets model
(distance on a sheet, distance between the sheets) are extended to any product
of two spectral triples. The distance between different points on different
fibres is investigated. When one of the triple describes a manifold, one find a
Pythagorean theorem as soon as the direct sum of the internal states (viewed as
projections) commutes with the internal Dirac operator. Scalar fluctuations
yield a discrete Kaluza-Klein model in which the extra metric component is
given by the internal part of the geometry. In the standard model, this extra
component comes from the Higgs field.
