CIKLIDA DYUPENA I KRIVYE VTOROGO PORYADKA. CHAST' 2
Abstract and keywords
Abstract (English):
Making smooth outlines produced products may be due to the different requirements: aerodynamic, structural, aesthetic, etc. Therefore, the consideration of the subject of curves of the second order is included in many textbooks on descriptive geometry and engineering graphics. These curves can be used as a transition from one line to another with the first and to the secondorder smoothness. In the first part of this work dealt with the General rules of construction of second-order curves based on the properties of ticlid Dupin. Used the total for all of Konik the principle of creation — the center of the sphere that is in contact circumferentially with ciklidas the clock, when you change the radius of the sphere moves along the curve of the second order. The circle of contact of the sphere with Cichlidae Dupin always located in a plane passing through one of the two axes of cyclide, and each of these planes intersects cyclide by two circles of contact. This property formed the basis of graphical representation, common to all curves of the second order. Thus was created a unified principle of construction, implemented a systematic approach. In addition, the building has a connection with such a conversion as the Central homothety or the like. It considers the construction of an ellipse with different variants of the task: two focuses and a point belonging to the hyperbola; two values: a and b; by the actual diameter of the hyperbola is 2a and its tricks; the size 2b of the hyperbola and its foci; the vertices of the hyperbola and the point to her belonging; largest 2b hyperbola and the point, owned her; the equation of the hyperbola; the contour of cyclide Dupin. Also, eight options were considered the task of constructing the parabola.

Keywords:
pairing, descriptive geometry, cyclic surfaces, canal surface, cyclide of Dupin, the task of Apollonius.
Text

Придание плавных очертаний изготовляемым изделиям может быть обусловлено различными требованиями: аэродинамическими, прочностными, эстетическими и т.д. Поэтому рассмотрение темы кривых второго порядка входит во многие учебники по начертательной геометрии и инженерной графике [1–4; 6; 8; 9; 11; 13–16; 18; 25–28; 30]. Разработанные принципы построения кривых второго порядка были основаны на свойствах циклиды Дюпена [7; 10; 12; 19–24; 31].

В первой части данной работы [23] рассматривались общие правила построения кривых второго порядка на основе свойств циклид Дюпена. Применялся общий для всех коник принцип построения — центр сферы, соприкасающийся по окружности с циклидой Дюпена, при изменении радиуса этой сферы перемещается по кривой второго порядка. При этом окружность соприкосновения сферы с циклидой Дюпена всегда расположена в плоскости, проходящей через одну из двух осей циклиды, а каждая из этих плоскостей пересекает циклиду по двум окружностям соприкосновения. Это свойство легло в основу графического построения, общего для всех кривых второго порядка. Таким образом, был сформирован единый принцип построения, осуществлен системный подход. Кроме того, все рассматриваемые построения имеют связь с таким преобразованием как гомотетия (центральное подобие) [5; 17; 29].

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