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Геометрия 7-9 класс تعارف

Geometry (from al-Greek.. Γῆ - Land and μετρέω - «measure") - a branch of mathematics that studies the spatial patterns, relationships and their generalizations.

Geometry as a systematic science emerged in ancient Greece, its axiomatic construction described in the "Elements" of Euclid. Euclidean geometry has been studying the simplest figures on a plane and in space, the computation of areas and volumes. Proposed in 1637 by Descartes coordinate method formed the basis of analysis and differential geometry, and tasks associated with mechanical drawing led to the creation of descriptive and projective geometry. Thus all construction remained within the axiomatic approach of Euclid. Radical changes associated with the work of Lobachevsky in 1826, which declined to the parallel axiom and created a new non-Euclidean geometry, thus determining the way of further development of science and the creation of new theories.

Classification geometry proposed by Klein in "Erlangen Program" in 1872 and containing basically invariant geometric objects with respect to different groups of transformations, continues to this day.

The geometry of the mutual arrangement of bodies involved, which is expressed in touch or adjacent to one another, the location "between", "inside", etc.; tel value, ie the concepts of equality bodies, "more" or "less"; and transformations of bodies. Geometric object is an abstraction since the time of Euclid, who believed that "the line is a length without width", "surface is that which has length and width." Point is an abstraction associated with a decrease in all the unlimited size of the body, or the limit of infinite division. Location, size and transform geometric shapes defined spatial relationships.

Exploring the real objects, geometry considers only their shape and relative position, abstracting from other properties of objects, such as density, weight, color. This allows you to move from the spatial relationships between real objects to any relationship and forms that arise when considering similar objects and similar spatial. In particular, the geometry allows us to consider the distance between the functions

Generally accepted today [citation needed 370 days] classify the different branches of geometry suggested Felix Klein in his "Erlangen Program" (1872). According to Klein, each section examines the properties of geometric objects that are preserved (invariant) under the action of certain groups of transformations specific to each section. According to this classification, in classical geometry are the following major sections.

Euclidean geometry, in which it is assumed that the size of segments and angles when moving figures in the plane do not change. In other words, it is a theory of the properties of shapes that are saved when their shift, rotation and reflection.

Plane geometry - Euclidean geometry section examining figures on a plane.

Geometry - section of Euclidean geometry, which studies shapes in space.

Projective geometry, which studies the projective properties of figures, that is, properties that are preserved under their projective transformations.

Affine geometry, which studies the properties of figures that are preserved under affine transformations.

Descriptive Geometry - engineering discipline, which is based on a projection method. This method uses two or more projections (orthogonal or oblique), which allows us to represent three-dimensional object on a plane.

 Spherical triangle

Modern geometry includes the following additional sections.

Multidimensional geometry.

Non-Euclidean geometry.

Spherical geometry.

Hyperbolic geometry.

Riemannian geometry.

Geometry of manifolds.