from 01.10.2008 until now
Russian Federation
In modern textbooks on analytical geometry the thought is missed out, how analytical geometry was developed. On the one hand, descriptive geometry formed much later than analytical geometry, and on the other hand, without elements of descriptive geometry was impossible to create a theory of analysis in geometry, although the first attempts of considering of geometry belong to the times of Ancient Greece. In the author´s opinion the development of the analytical calculations have served a variety of images, including orthogonal and axonometric projections. As descriptive geometry is the theory of images, it thus follows that descriptive geometry was the basis for creating of the analytical geometry. In the proposed work it is proved by the simple and clear. When the images in plane are viewed, we are dealing with a 2D drawing with simple planar geometric figures. There is no presence of descriptive geometry, although some of our "partners" considers the descriptive geometry as geometry on a plane. Let´s leave this confusion on their conscience. But as soon as we deal with space, we cannot do without the axonometric drawing, and axonometry is a section of descriptive geometry. So we can predicate, that analytic geometry is based on descriptive geometry. On the basis of predetermined outcome criterion of geometric shapes — belonging of point to this geometric figure, it is possible to obtain equations of various geometrical figures. This condition is used for the analytical derivation of the equations. There are examples of receiving through the orthogonal projections of various geometric shapes their analytical equations — equations of a straight line, plane, surfaces of rotation (sphere, ellipsoid, paraboloid, conical surfaces of rotation, one-sheet hyperboloid, duopolistic hyperboloid); position and metrical tasks are considered.
geometry, descriptive geometry, analytical geometry, higher education, geometric education.
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