What is geometry? Physical geometry and mathematical geometry as two

aspects of the proper Euclidean geometry.

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://www.ipmnet.ru/~rylov/yrylov.htm

Updated December 18, 2013

abstract

Primordially a geometry was a science on properties of geometrical objects and their mutual disposition. Such interpretation of the term "geometry" is qualified as physical geometry. A use of only Euclidean geometry generated another interpretation of the term "geometry", which was interpreted as a logical construction. Such interpretation of the term " geometry" is qualified as mathematical geometry. Mathematical geometry cannot use for description of the space-time, generally speaking. Nevertheless the mathematical geometry has been used for description of the space-time during the twentieth century. This circumstance lead to problems in general relativity.

There is text of the paper in English (pdf, ps) and in Russian (ps, pdf)