Euclidean geometry as algorithm for construction of generalized

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
 Web site:
or mirror Web site:

Updated November 21, 2005


It is shown that the generalized geometries may be obtained as a deformation of the proper Euclidean geometry. Algorithm of construction of any proposition S of the proper Euclidean geometry E may be described in terms of the Euclidean world function sigma_E in the form S(sigma_E).  Replacing the Euclidean world function sigma_E   by the world function sigma of the geometry G, one obtains the corresponding proposition S(sigma)  of the generalized geometry G. Such a construction of the generalized geometries (known as T-geometries) uses well known algorithms of the proper Euclidean geometry and nothing besides. This method of the geometry construction is very simple and effective. Using T-geometry as the space-time geometry, one can construct the deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a
space-time geometry defined properly (with quantum constant as an attribute of geometry) allows one to explain quantum effects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles).

There is text of the paper in English and in Russian