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- W2617366410 abstract "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." @default.
- W2617366410 created "2017-06-05" @default.
- W2617366410 creator A5056375304 @default.
- W2617366410 creator A5069364839 @default.
- W2617366410 date "2015-04-17" @default.
- W2617366410 modified "2023-09-23" @default.
- W2617366410 title "Properties of Cyclide Dyupen and Their Application. Part 1" @default.
- W2617366410 doi "https://doi.org/10.12737/10454" @default.
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