THE ANALYSIS OF ANALOGUES OF GEOMETRICAL MODEL OF THE DETERMINATION THE PARAMETERS OF AN INACCESSIBLE POINT

Abstract

The present work analyses of the analogues of the geometric model developed for the determination of the parameters of the inaccessible point of an object. The common issues are revealed and essential steps of their resolution are identified. The essence of the problem is that the unavoidable contradiction between the need of obtaining the exact value of the determined parameter and an error involved in any measurement. The purpose of the present work is to investigate a possibility of use of the known analogues of the geometrical model of the determination of the parameters of the inaccessible point of an object. It is achieved in two steps: 1. The analysis of the known analogues of the geometrical model of the determination of the parameters of the inaccessible point of an object. 2. The determination of a feasible variant of the geometrical model of experimental measurements.

The present study considered the analogues of the geometrical model of the determination of the parameters of the inaccessible point of an object. Phales Miletsky (640/624-548/545 BC) used similarity of triangles for the determination of the distance from coast to the ship and pyramid height in Egypt. For the determination of parameters of an inaccessible point by means of a theodolite, a flat analogue is the geometrical model of two overlapped rectangular triangles. Trigonometrical relationships for the determination of the values of required parameters are discussed.

The pros and cons of the known analogues are identified. It is revealed that, in the analyzed geometrical models, all the measurements of the reference values of parameters are carried out with some errors in one plane. Therefore, a theoretically correct solution of the problem is in some domain (area) of the real result. The domain of possible results takes the shape of a trapeze. Besides, result of direct measurements, as a rule, are fractional numbers. Therefore, it is virtually impossible to obtain one exact result.

The feasible variant of geometrical model of performance of measurements and processing of results is defined. It is suggested to develop complex three-dimensional geometrical and analytical models of definition of area (domain) of the value of parameter of the inaccessible point of an object.

Keywords: a building, a roof, the analysis, directional ray, collimating ray, measurement of coordinates of a point, geometrical model, analogue.