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.
On the number of rational points of a plane algebraic curve
