Purpose. Study of geometric transformations. We will consider the so-called point transformations of space. Methodology. The most important are one-to-one transformations. They allow exploring and studying the properties of the transformed object using the properties of the original object (line, surface and figure) and the properties of the transformation. Cremona transformations occupy a special place in the set of one-to-one nonlinear transformations. Construction of one-parameter (stratifiable) transformations is carried out as one-parameter set of plane transformations, both linear and non-linear ones. The plane, in which the specific transformation is prescribed, moves in space by a certain law forming a one-parameter set of planes. The set of such plane transformations makes up the space transformation. Findings. The designed graphics algorithms and the established transformation equations allow building the visual images of transformed surfaces and conducting their research by analytical geometry methods. Originality. By completing elementary algebraic transformations of this equation, we obtain the cissoids equation. If the plane φ is continuously moved parallel to itself, it results in occurrence of surface, whose carcass will be the set of cissoids and the set of front-projecting lines. Practical value. The considered set of stratifiable algebraic transformations gives an effective means for exploring new curves and surfaces obtained by transforming the known algebraic lines and surfaces. These graphic algorithms allow graphically depicting the transformed lines and surfaces. The considered procedure of drawing up analytical formulas of specific transformations allows us to study the transformed surfaces and lines using the methods of analytic geometry. The above transformations can be of arbitrary high order, which is especially important during the design of complex technical surfaces such as aircraft components, parts of water and gas turbines, supports of the structures subject to strong flow of liquid, etc. Space modelling issues, including the building of graphic plane models of space, are relevant both in theoretical terms and in terms of application of the non-linear surfaces investigated on their basis for constructing the technical forms of parts and aggregates of construction machine movable elements, the middle surfaces of shells, the surfaces of turbulent blade, etc.
The technology of mortar injection into a concrete element of construction is developed in the paper. The different methods of applying the repair polymeric mortar on the base of alkylrezorcine on concrete surface of a construction, which are used depending on damage rate of the construction and provides high level of adhesion to concrete, are presented.
The comparison of classical and computer testing system is given in the article. The effect of usage of «Prometey» remote education system is analyzed. The positive effects of passing the Module Tests by students are shown.
In the article the most common methods for approximate involute of sphere are considered and analyzed. The examples and sequential performance are presented.
Purpose. The aim of this work is to study quasilinear space models. Methodology. Questions of space modeling, including the construction of graphical models of planar space are actual both in theoretical terms and in terms of their application investigated on basis of nonlinear surfaces to construct forms of technical details and units of construction machinery, middle surfaces of shells, turbulent surfaces of the blades etc. Findings. The article solves the following problems: 1. what requirements must satisfy projecting curves as well as what type of curves can be used to create a quasi-linear model of the space; 2. spatial transformation generated by kvazimodelyu convert twoJoint-substituted spaces and filed constructive ways to implement this transformation on the diagram Monge were investigated. Practical value. The considered conversion of space can be used for the construction of technical forms, surfaces of complex parts and designs for the construction of tunnels and bridges.
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