Geometry (Greek. ?????????; geo - earth, meter - measurement) - area of mathematics, studies geometrical bodies and their features, from the most simple (such as distance, square, goniometry), to more complex (such as the curvature, fixed point, or size). Depending on the type of spatial structures can talk about different types of geometry.
Euclidean geometry is engaged primarily study invariants (constant properties), isometric (distance compliance) and similarities (corners preservation). Affine Geometry investigates the invariants of affine transformations, and projective geometry describes the invariants of projective transformations. These problems are generalized to other objects (eg, Riemann space, or metric spaces). invariants research method is the main method of investigation of more complex mathematical objects (such as topological spaces, abstract groups, rings, and so on. d.)
Geometry, as arithmetic – one of the oldest sciences. Like other branches of mathematics geometry developed from the study of figures, known from everyday life.
Euclid's axioms
Geometry originated in ancient times. In the beginning it was a set of rules for the measurement of material objects. The first attempts to formulate the theorems of geometry, It appeared in the VI century BC, in ancient Greece (Fales from Miletus). A large contribution to the study of the geometry of a III century BC. e. Euclid has made work “elements” (OK. 300 BC. e.). It included the proportion of theory, arithmetic and simple Geometry of formula, and is the first report on the geometry in the history of mathematics. All statements in it derived in accordance with the traditional rules of logic based on the received primary concepts and axioms. It is also the first axiomatic theory in the history of mathematics.
The turning point in the development of geometry was the work of the French mathematician René Descartes, in the XVII century, (1637 city). They laid the foundation for the development of analytic geometry. In the Descartes introduced into geometry algebraic calculation methods. known, that a little earlier it is also made by Pierre de Fermat, which, however, did not publish his results.
