Особенности свойств параболы при ее моделировании

Abstract

When studying the theory of contour construction in “Affine and Projective Geometry” course on educational program specializations “Computer-Aided Design Systems” and “Applied Informatics in Design” a unit of computational and graphic task "Contour Construction" is carrying out in structural design. In this computational and graphic task the contour constructions are carrying out by second-order curves (a circle — by the radius and graphical method; a hyperbola, an ellipse, a parabola — by means of Pascal curves, taking into account positions of engineering discriminant). The constructions of an arc of ellipse, hyperbola, and parabola are carried out based on Pascal theorem: in any hexagon, which vertices belong to a second-order series, three points of the opposite sides’ intersection lie on one straight line — the Pascal line. However, in construction of a conic (a second-order curve), it is necessary to draw students’ attention to the fact that the points belonging to a second-order series (a second-order curve, or a conic) make a geometrical locus of intersection of Pascal hexagon’s adjacent opposite sides. By this method students successfully construct conjugate arcs of an ellipse and a hyperbola with other conics. The construction of a parabola arc, conjugated with other conics, is carried out by the method of engineering discriminant (it is more convenient to divide line segments in halves: a median and a triangle side, which is opposite to its vertex lying on a parabola arc). It should be noted that theoretical and practical material on this subject corresponds to the assimilation of Study Plan’s necessary competences (in accordance with each educational program), however, some aspects of this subject are accepted by students simply by trust. The aim of this paper is research of construction methods for parabola, applied to contour simulation.