Abstract and keywords
Abstract (English):
In the first part of work was addressed mainly the issue of properties under Dupin cyclide, and given some examples of their applications: three ways of solving the problem of Apollonius using only compass and ruler, using the identified properties of Dupin cyclid. The second part of work continued with consideration of the use of property under a lie of Dupin. It is determined that the focal surface of cyclid of Dupin is degenerated in the lines and represent curves of the second order. Here under a lie can be defined conic curve and a sphere whose center lies on the focal curve. Polyconic conformity these focal curves is revealed. The article show the formation of the surface of the fourth order on the basis of defocusing curves of the second order. In this issue of the journal the reader is invited to consider the practical application of properties under a lie of Dupin for example of well known problems with on-voltage. If the first part of the work was cited only three ways of solving the problem of Apollonius, in the third part the author considers other possible mates: as at zero the size of the radius of the circle and the demon is of course great. All decisions – both known and not really based on properties of Dupin cyclide. In the course of engineering graphics, introductory tests, as they say now, drawing on architectural faculties there are tasks, dedicated to the mating arcs of circles with straight lines, and circles passing through the points in various combinations. Therefore, the proposed practical application cannot be considered far-fetched – it is based on the practical utility of method.

pairing, descriptive geometry, cyclic surfaces, canal surface, Dupin cyclide, the problem of Apollonius.

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