# Tasks of building

The first **tasks of building** originated in ancient times. They emerged from the economic needs of the person. Already the ancient architects and surveyors had to solve simple problems on construction related to their profession.

The very first task to build, apparently resolved directly on the ground and consists of making the straight lines and the construction of a right angle.

The tasks of building resorted ancient engineers were working when a drawing of a plant and to deal with finding a beautiful geometric forms and structures of its greatest capacity. Tasks to build helping people in their economic life, their decisions formulated in the form of "practice" on the basis of visual reasons. These problems were the basis for the emergence of visual geometry, which found a fairly extensive development of the ancient peoples of Egypt, Babylon, India and others.

However, rules of thumb first land surveyors, architects, astronomers have not yet accounted for the present geometry as a deductive science, based on the theoretical constructs and evidence. Tasks to build widely spread in ancient Greece, where the first established in the geometric theory of systematic exposition.

The first Greek scientist who examined geometrical problems to build, was Thales of Miletus. It was he who, taking advantage of the construction of the triangle to determine the distance, inaccessible to direct measurement - from shore to ship in the sea. He's calculated the height of the Egyptian pyramids by the shadow cast by it.

Tasks to build interest and Pythagoras. Pythagoras and his disciples spent a lot of energy to separate the geometric data consisting of time before a set of intuitive rules that give the character of this science, based on the logic of speculative evidence. Particularly hard task to build interest of Plato, founder of the famous "Academy" in Athens. Plato and his disciples believed geometric construction, if it is performed with the help of a ruler and compass, t. E. By means of circles and straight lines. If in the process of building used other drawing instruments, the construction was not considered geometry. The ancient Greeks followed Plato sought to geometric constructions and considered them ideal in geometry.

Already in ancient Greek mathematicians met with the three objectives of building that could not be the solution. These tasks are the following:

**The first task.**It is required to construct a cube edge, which would have a volume twice as much of the cube.*The task of doubling the cube.***The second challenge.**Requires arbitrary angle into three equal parts.*The problem of the trisection of an angle.***The third task.**It is required to construct a square whose area is equal to a given circle.*The problem of squaring the circle.*

These three tasks to build and carry the name of "famous geometric problems of antiquity".

A major role in the problem of the construction of play in the "Elements" of Euclid (3 century BC), Where the figures proved the existence of their construction with the help of a ruler and compass. In the "beginning" of Euclid are almost all the problems on construction, which is currently being studied at school.