Tatyana Myrashkina

The relevance of the work is due to the fact that conical surfaces are one of the main types of surfaces on which all constructions in geometry and engineering graphics are based. Students learn the concept of "cone" in high school, but they study it in more detail only when they enter technical universities. Conical surfaces play an important role in human life. Roofs of buildings, architectural structures and technical facilities are designed on the basis of these surfaces. This article describes such concepts as conical surfaces, cones, their basic properties and construction features. This article may be interesting for high school students, first and second year students of technical universities, and teachers of descriptive geometry and mathematics.

The relevance of this work relates to the special place of the lines and surfaces of the second order in the courses of analytical geometry and engineering graphics at the technical University. Parabola and corresponding to it in three-dimensional world paraboloid, play an important role in many physical processes. As a result, they have found wide application in many engineering, technical and other devices, architecture, and just in everyday life. In this article, the authors examine the mathematical properties of parabola and paraboloid and the peculiarities of their graphical representation. The content of the article will be interesting for students of engineering and mathematics, teachers of mathematics and engineering graphics, as well as for high school students preparing to enter universities to study technical or mathematical sciences, since prospects of modern school education development are associated with the growing role of its polytechnic component.