General Principles for Formation of Ruled Surfaces. Part 3

Abstract

We continue to consider the formation of ruled surfaces with a single method of their formation. In the first and second parts have been introduced more than forty options for specifying surfaces. These formations with the help of guide lines and surfaces are considered in a new aspect – as formation in science and production of all of ruled surfaces. In this paper, we consider new options for specifying ruled surfaces. Generalized the task for torso surface. If in textbooks on descriptive geometry torso surface is given as 1∞ straight lines, tangent to the spatial line, the proposed version of the are considered three guides: two curves (surface) plus a plane touching to both curves (surfaces). It is shown that three guides are also required to set screw ruled surfaces. The concept of a limit ruled surface is introduced to determine the region of existence of ruled surfaces. The table of the simplest geometrical figures for obtaining congruences is given. A number of examples of congruences obtained by using two guides are given. All these examples once again confirmed the validity of the law of assignment of ruled surfaces using three guides and three geometric conditions characterizing the ratio of the forming line to these three guides. The three geometric conditions are the contact of the forming line to the guide surface and the intersection of the forming line with the guide line. The proposed task of ruled surfaces can be used in the consideration of ruled surfaces in lectures on descriptive geometry and other geometric disciplines.