Properties of Cyclide Dyupen and Their Application. Part 1

In the training course in descriptive geometry we consider the class of surfaces formed by circles and named Circular surface. Within this class of surfaces is the so-called kanalowe surface. Under a lie cyclide belong to canalave surfaces, but in the course of descriptive geometry, their formation is not considered. Under a lie cyclide were discovered by Pierre Charles Francois Dyupen in the early nineteenth century and named in his honor. He dyupen was a disciple of Gaspard Monge, like many great scientists in France at that time. Under a lie cyclide usually represented as envelopes of a family of spheres tangent to three given. Under a lie – the only surface whose focal surface degenerates into a line, and all lines of curvature are circles. Particular cases of ticlid cyclide is a torus, and conical and cylindrical surfaces of revolution. The paper discusses the analytical representation of the focal lines for the General case of a job under a lie cyclide. It is analytically proved that the contact line inscribed in cyclide spheres are circles, and degenerate in the focal curve on the surface is a curve of the В учебном курсе начертательной геометрии из- учается класс поверхностей, образованный окруж- ностями и названный «Циклические поверхности» 5; 8; 12. Внутри этого класса поверхностей есть так называемые каналовые поверхности. Циклиды Дюпена принадлежат к каналовым поверхностям, более того, они являются частным случаем 2–4; 6 этих поверхностей, но в курсе начертательной гео- метрии их формирование не рассматривается. Циклиды Дюпена были открыты Пьером Шарлем Франсуа Дюпеном (1784–1873) в начале XIX в. и названы в его честь 14. Дюпен (рис. 1) был учени- ком Гаспара Монжа, как и многие великие ученые Франции того времени, и являлся почетным членом Петербургской академии наук c 20 декабря 1826 г. second order. Identified some (nine) properties of this surface. As a practical application of ticlid cyclide solved such well-known classical problem as the problem of Apollonius (about Casa-NII three circles fourth) and task Farm (touch four spheres fifth) using again the classic way – with a ruler and a compass. In the first part of the article is only three ways to solve the problem of Apollonius solely by means of compass and ruler, using the properties of cyclide Dyupen.