from 01.10.2008 until now
Russian Federation
When solving large geometric problems, in some cases there is a need to solve smaller auxiliary problems. So, when expanding the options for forming ruled surfaces, a solution arose for constructing a plane or a straight line at certain angles of inclination to the planes of projections or to some given plane of general position. The article presents this related task of constructing a plane, as well as building a straight line using a sphere. The basis for constructing a plane and a straight line at certain angles to the projection planes is the application of a contiguous cone of rotation to an arbitrarily specified sphere. The same method is already used to construct a straight line and a plane to a given plane of general position, taking into account that this plane is tangent to some given surface. All constructions of linear surfaces are based on the principle of specifying three guides and three conditions limiting each of the generators in relation to the specified guides. The condition of passing the guide at certain angles to the surfaces expands the possibilities of designing ruled surfaces almost indefinitely.
geometry, engineering geometry, kinetic geometry, descriptive geometry, metric tasks
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