### Euclidean geometry as algorithm for construction of generalized

geometries.

#### Yuri A. Rylov

*
**Institute for Problems in Mechanics, Russian Academy of
Sciences*

* 101-1 ,Vernadskii Ave., Moscow, 119526, Russia*

* email: rylov@ipmnet.ru*

Web site:
http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm

or mirror Web site:
http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm

Updated November 21, 2005

#### abstract

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__,