Свойства циклид Дюпена и их применение. Часть 3: сопряжения

Abstract

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.