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Geometric constructions


Construction issues, or geometric constructions. Construction of geometrical figures that meet different conditions, with the help of different tools (one-sided mathematical linear, double sided divider, right-angle model, and other tools). The section of geometry that learns the methods of geometrical configurations is called constructive geometry. Configuration issues are learned in Euclidean geometry and in other geometries (spherical geometry, Lobachevsky geometry, etc.). These problems are considered both on the plane and on the space.
Classic tools of construction are divider and linear. But constructions with only a divider (Mor-Maskeroni configurations), with two-sided linear, with a right angle (a right-angle model) and other tools are also considered. All construction problems are based on axioms of constructive geometry.
All construction issues are based on axioms of constructive geometry. The axioms of the constructive geometry are the simplest geometric arrangements. If the solution of c.p. is brought to the finite number of simple constructions, it is considered to be solved.
Naturally, each construction tool has its own constructive power. That is, each construction tool has a certain postulates system.
For example, it is known that it is not possible to divide the section to two equal parts by a linear only, but it is possible to do it with the help of a level.

Source: Misir Mardanov, Sabir Mirzayev, Shabala Sadigov, The book “The mathematical explanatory dictionary of for pupils”, Baku, 2016.

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