Abstract: Poincaré asserted that any non-Euclidean geometry can and should be reduced to Euclidean one by correcting physics.
However, Einstein proposed to describe gravity using Riemannian geometry. From the viewpoint of Poincaré, this was
an unreasonable step that can lead physicists into mathematical jungles. In this paper we used Euclidean geometry
instead of Riemannian geometry. To do this, we introduced a new universal law of compression and expansion of all
bodies, including atoms, in a gravitational field. In the case of a weak field, a new approach leads to the same equation of
motion as in general relativity. In the case of a strong field, a new approach allows us to solve the problem of black holes
and the problem connected to Mach\'s principle. An experiment with atomic clocks is proposed, which will allow us to
determine whether geometry in a gravitational field really becomes Riemannian or it remains Euclidean.