Приложение свойств циклиды Дюпена к изобретениям

Abstract

Dupin cyclide belongs to channel surfaces. These surfaces are the single known ones whose focal surfaces, i.e. surfaces consisting of point sets of centers of curvatures, have been degenerated into two confocal second order curves. In the works devoted to Dupin cyclide and published in the "Geometry and Graphics" journal, are presented various cyclides’ properties and demonstrated application of these surfaces in various industries, mostly in construction. Based on Dupin cyclides’ properties have been developed several inventions relating to drawing devices and having the opportunity to apply in various geometric constructions with the use of computer technologies. It is possible because the Dupin cyclides’ geometric properties suppose not only to create devices recognized as inventions, but also provide an opportunity to apply these properties to write programs for drawing v arious kinds of curves on a display screen: the second order curves, their equidistant in the direction of normals or tangents, as well as to perform other constructions. It should be said that in inventions belonging to technical areas, which include the drawing devices, the geometric component is always decisive. This position with the express aim of technical inventions can justify any copyright certificate of the USSR, any patent of Russia and foreign countries. Unfortunately, currently in schools geometry is not studied as a component of pupil’s intellectual horizons, that broadens his area of interests and teaches to analytical understanding the world, but as an inevitable, almost unnecessary appendage in preparation for the Unified State Examination.