General Principles for Formation of Ruled Surfaces. Part 2

Abstract

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.