  After reading such a question, any mathematician will say that, according to
a well known result of L.P. Eisenhart found in 1926, the answer is " One " of
course, namely the only constant allowing to describe the so-called " {\it
constant riemannian curvature} " condition. The purpose of this paper is to
prove the contrary by studying the case of two dimensional riemannian geometry
in the light of an old work of E. Vessiot published in 1903 but {\it still
totally unknown today} after more than a century. In fact, we shall compute
locally the {\it Vessiot structure equations} and prove that there are indeed "
Two " {\it Vessiot structure constants} satisfying a single {\it linear Jacobi
condition} showing that one of them must vanish while the other one must be
equal to the known one. This result depends on deep mathematical reasons in the
formal theory of Lie pseudogroups, which are involving both the Spencer
$\delta$-cohomology and diagram chasing in homological algebra. Another similar
example will illustrate and justify this comment out of the classical tensorial
framework of the famous " {\it equivalence problem} ". The case of contact
transformations will also be studied. Though it is quite unexpected, we shall
reach the conclusion that the mathematical foundations of both classical and
conformal riemannian geometry must be revisited. We have treated the case of
conformal geometry in a recent arXiv preprint.

Differential Geometry