Loci of points (LOP) equally spaced from two given geometrical figures are considered. Has been proposed a method, giving the possibility to systematize the loci, and the key to their study. The following options have been considered. A locus equidistant from N point and l straight line. N belongs to l. We have a plane that is perpendicular to l and passing through N. N does not belong to l – parabolic cylinder. A locus equidistant from F point and a plane. In the general case, we have a paraboloid of revolution. The F point belongs to the given plane. We get a straight line perpendicular to the plane and passing through the F point. A locus equidistant from a point and a sphere. The point coincides with the sphere center. We get the sphere with a radius of 0.5 R. The point lies on the sphere. We get the straight line passing through the sphere center and the point. The point does not coincide with the sphere center, but is inside the sphere. We get the ellipsoid. The point is outside the sphere. We have parted hyperboloid of rotation. A locus equidistant from a point and a cylindrical surface. The point lies on the cylindrical surface’s axis. We get the surface of revolution which generatix is a parabola. The point lies on the generatrix of the cylindrical surface of rotation. We get a straight line, perpendicular to that generatrix and passing through the cylinder axis. The point does not lie on the axis, but is located inside the cylindrical surface. We get the surface with a horizontal sketch line – the ellipse, and a front sketch lines – two different parabolas. The point is outside the cylindrical surface. A locus consists of two surfaces. The one with the positive Gaussian curvature, and the other – with the negative one.

In this paper are studied surfaces which are loci of points (LOP) equally spaced from a point and a conical surface under a variety of the point and conical surface’ mutual arrangement. Mathematical models of such surfaces are studied, and mathematical analysis of their properties is performed, as well as 3D models of considered surfaces are constructed. Possible cases of mutual arrangement for the point and the conical surface: • the point is at the conical surface’s vertex; • the point is on the conical surface; • the point is inside the conical surface: –– on the axis, –– not on the axis; • the point is outside the conical surface. The point is on the vertex of the conical surface Γ — the obtained conical surface Ω has the same vertex, whose generatrixes are perpendicular to the generatrixes of the surface Γ. The point is on the conical surface Γ — LOP equally spaced from the surface Γ and the point O separates into a straight-line l and a surface Φ of 4th order. The line l is located in the axial plane passing through the point O and is perpendicular to the generatrix of the conical surface Γ. Obtained surface Φ has a symmetry plane passing through the axis of the conical surface Γ and the point O. Many sections of the obtained surface Φ are Pascal snails. The point is inside the conical surface on the axis. Obtained surface α is a rotation surface, and the axis z is its axis of rotation. All the sections of the surface by planes perpendicular to the axis z are circles. Point is outside the conical surface. A very interesting surface Ω has been obtained, with the following properties: the surface Ω has a support plane, which is tangent to the surface Ω on a hyperbole; the surface Ω has 2 symmetry planes; there are a circle, parabola and Pascal’s snail among the surface Ω sections. In this paper have been considered analogues between surfaces of LOP equally spaced from the cylindrical surface and the point, and from the conical surface and the point.

The loci (L) equally spaced from a sphere and a straight line, and from a conic surface and a plane, are considered. The following options have been considered. The straight line passes through the center of the sphere (a = 0), at the same time completely at spheres’ positive radiuses a surface of rotation is obtained, forming which the parabola is, and a rotation axis – this straight line. The parabola’s top forms the biggest parallel on the site points of intersection of the parabola’s forming with the rotation axis. Let's call such paraboloid a perpendicular paraboloid of rotation. The straight line crosses the sphere, but does not pass through the center (0 < a < R/2) – a perpendicular paraboloid, at that the surface is also completely obtained at radiuses’ positive values. The straight line is tangent to the sphere (a = R/2) – a surface which projections are parabolas, lemniscates and circles, and a piece from a tangency point to the sphere center – at radiuses positive values; a beam from the sphere center, perpendicular to this straight line – at radiuses negative values, at that the beam and the piece belong to one straight line. The straight line lies out of the sphere (α > R/2) – two different surfaces, having the general properties with a hyperbolic paraboloid, are obtained, one of which is obtained at radius positive values, and another one – at radius negative values. It has been noticed that loci, equally spaced from a sphere and a straight line, and from a cylinder and a point, coincide at equal radiuses and distances from axes to points and straight lines if to take into account the surfaces obtained both at positive, and negative values of radiuses. Locus, equally spaced from the conic surface of rotation and the plane, are two elliptic conic surfaces which in case 7.4.1 degenerate in the conic surfaces of rotation. In cases 7.4.3 and 7.4.4 one elliptic conic surface degenerates in a plane and a parabolic cylinder respectively.

In May 2018 the Engineering Graphics Chair celebrates 90 years from the date of its foundation. The Chair was organized in 1928. The paper tells the Chair’s history, its teachers and heads, as well as a brief description of its scientific work. In 1900 were established the Moscow Higher Feminine Courses (MHFCs). A year after the October revolution, in late 1918, MHFCs were transformed into the 2nd Moscow state University. In 1930 the 2nd MSU was reorganized into three independent institutes: medical, chemical-technological and pedagogical ones. In May 1928 was organized the Chair of Technical Drawing, this moment is the counting of Engineering Graphics Chair existence. The first head of the Chair was S.G. Borisov. Than the Chair was supervised by Associate Professor A.A. Sintsov (from September 1932 till January 1942), Associate Professor M.Ya. Khanyutin (in 1942–1952), Associate Professor N.I. Noskov (in 1954–1962), Associate Professor F.T. Karpechenko (in 1962–1972), Senior Lecturer N.A. Sevruk (in 1972–1982), Professor, Doctor of Engineering E.K. Voloshin-Chelpan (from January 1982 to August 2007), Associate Professor V.I. Vyshnepolsky (from August 2007 till present). Currently, on the Chair are carrying out researches in the following directions: Higher School’s Pedagogy; Academic Competitions of Regional and All-Russia’s Level; Loci; Geometry of Cyclic Surfaces; Theory of Kinetic Geometry; Geometries; Geometric Transformations; Theory of Fractals; Famous Geometers’ Biographies.