In technical inventions related to innovative developments, the role of one of the main components belongs to geometry. A follow hypothesis has been adopted: in technical inventions the geometrical component is the determining one. This hypothesis applied to technical inventions can be confirmed by any copyright certificate, any patent both in Russia and abroad. In proposed paper this statement is proved by examples developed based on geometry of following inventions. 1. Screen feeder for sticky masses. Screen feeder’s grates are made in pairs, and between grate pairs there are gaps for screening of material’s size-defined fractions. In the screen-feeder has been proposed such geometry of grates that grates of each pair could clean each other, thereby preventing sticking on the surface and destroying the gaps between the pairs, which transforms the usual screen-feeder with cylindrical grates at an ordinary feeder. 2. Double-screw mixer for paste-like masses. The mixer consists of two contiguous worms. Their surfaces are the helical ones, in cross-section consisting of two quarters of circles stacked at the ends. Such cross-section allows homogenize the mixed paste-like material in the best way, and also deliver it under higher pressure in an extrusion head, that improves a final product. 3. Machine for processing of multi-faceted surfaces. This invention serves for manufacture of worms with a cross-section composed of two, three, etc. pieces of circles of the same radius and angle. Worms, made with this machine, are designed for the above mentioned two-screw mixer. 4. Method of mechanical processing. This method is also intended to manufacture of worms for two-screw mixer.

Geometric Simulation and Descriptive Geometry

The Geometric Component Of Technical Innovations

Formation of Surfaces Under Kinetic Displaying

In this paper the consideration related to formation of ruled surfaces with a single method for their set up that was proposed in the first part of the work, is continued. In the first part of the work were considered more than twenty variants for set up of ruled surfaces, including four set ups by guide lines, overall known in the literature, for example, in the books of S.A. Frolov, A.V. Bubennikov, M.Ya. Gromov. However, the set up of ruled surfaces with the help of guide lines was proposed in a new aspect – as a constituent of a single method for setting absolutely all ruled surfaces, taking place in science and industry, and with additional variants. Besides, have been proposed equation systems, which solution leads to generation of equation for the given ruled surface. New set ups of ruled surfaces have included eighteen examples, which is the main material of the work’s first part. Also was proposed a table in which have been put all possible variants for set up of geometric figures’ guiding lines to obtain ruled surfaces. Of course, the proposed variants of guiding lines’ combination were presented in the enlarged form. In the proposed paper have been considered new, not presented before, variants for set up of ruled surfaces. Have been presented 19 examples, including the ones with one or two guiding planes, as well as when the guiding line belongs to one of guiding surfaces. Such surfaces can be considered as ruled surfaces of smooth transition. As in the first part of the work, the equation systems leading to the equation of the set ruled surface are proposed.

General Principles for Formation of Ruled Surfaces. Part 2

Probably, it is impossible to find such industry where the ruled surfaces would not be used. They are used in agriculture, in the heavy and light industries, in construction, in aircraft manufacturing, and in military art. Ruled surfaces are used in the design of wings, tail and partially fuselage of aircraft, car bodies, in the project engineering of slopes and embankments of auto-roads, abutments of bridge supports, transitions from a vertical quay to inclined walls of embankments, various hydraulic structures, towers, masts, cooling towers, vaults and arches, overlaps of pavilions, circuses, stadiums and other building structures, as well as in the calculation of solar exposure. This paper deals with the formation of ruled surfaces in a single method of their definition. A number of examples for definition of ruled surfaces have been presented. These examples show that in general for definition of ruled surfaces it is required to have three guides and three geometric conditions characterizing the position of a rectilinear generator with respect to each of the guides. Both surfaces and lines can act as guides. The plane is selected separately from other surfaces. The geometric conditions are the intersection with the guide line and the tangent or intersection at a certain sharp angle with the guide surface. The table of 19 variants for guides has been given. An attempt to classify surfaces does not even consider in this paper since it is impossible to classify ruled surfaces, even within its class, due to the lack of a criterion showing their belonging to one or another species. It can be concluded that the classification of surfaces may be used only for educational purposes and in cases where the surface name is obvious.

General Principles for Formation of Ruled Surfaces. Part 1

In the 2017-18 and 2018-19 academic years, in Moscow State Academic Art Institute named after V.I. Surikov a two-year experiment for architecture students on determination variances in different approaches to teaching methods for geometric education was conducted. The experiment was caused by the fact that many teachers believe that if there are computers in the Institute, it is necessary to use graphic programs as soon as possible – immediately introduce students to work on the computer even without allocating hours for this. No one wants to prevent implementation of computers, but we must not forget some nuances related to high technology. As in any case connected with complex hardware unknown for future users, here at the University, at the beginning it is also necessary to teach students how to work with the graphics program itself, and only then allow them perform geometric problems. You can give such an example: put an untrained person at the control panel of interceptor missiles and force him to shoot down a border trespasser in combat conditions. They will notify us that we are engaged in voluntarism. However to put an untrained student at a computer and forcing him to solve a purely geometric problem immediately is not voluntarism. Is it? \nThe experiment had showed that a student, even if he knows how to solve a particular problem, is not ready at all to perform it immediately on a computer in a graphic software. He begin to lose a lot of time getting familiar with the program and only after obtaining at least a minimum of knowledge about working with this program becomes ready to start the task.

Geometric Simulation and Descriptive Geometry

Citations

The Geometric Component Of Technical Innovations

Formation of Surfaces Under Kinetic Displaying

General Principles for Formation of Ruled Surfaces. Part 2

General Principles for Formation of Ruled Surfaces. Part 1

Quality of Geometric Education in Various Approaches to Teaching Methods

Related Papers (5)

Descriptive Geometry — the Base of Computer Graphics

Descriptive Geometry As Theory of Images

Modern Russian language: Morphemics. Word-formation

Parametric Geometry in Geometric Modeling

Place of Descriptive Geometry in the System of Geometric Education of Technical Universities