О задачах начертательной геометрии с мнимыми решениями

Abstract

The article is devoted to the discussion of the scientific
 methodological problems of presentation tasks of descriptive
 geometry along with having real and imaginary solutions. Examples
 of such problems are given, graphics solutions who give the wrong answers. As a consequence they resulted in some the textbooks on
 descriptive geometry to the emergence false claims type “ the curve
 degenerates to a point”, “a torus is a surface of the second order”,
 “conical and cylindrical surfaces are a special cases of the torsoboy
 surface in the case of degeneration of the ribs return torsoboy the
 surface at the point, etc.”
 In the article gives a correct mathematical interpretation of
 imaginary solutions the tasks by considering of examples an the
 determine the order and class of plane algebraic curve, the isolated
 point touch, of the line of intersection of surfaces of the second
 order with a common plane of symmetry. To obtain a mathematically
 valid answers the conclusion about the need for a combination
 of graphical and analytical solutions. This approach meets the
 requirements of the GEF on ensure as intrasubject discussed in this
 publication, and so interdisciplinary competencies. The latter have
 a broad outlet of descriptive geometry in complex space in the
 theory of algebraic curves and surfaces, kremenovic transformations,
 field theory, etc.