Ex. 3 Read and translate the following text

GEOMETRY AND TOPOLOGY

Ex.1 Practise the pronunciation of the following topical words checking it with your English-Russian dictionary if necessary

Ex.2 Translate the following word combinations into Russian

ancient branch of mathematics, Greek mathematician Euclid, collectively called, advanced arithmetic, Euclidean geometry, theorem of Pythagoras, point-set topology, combinatorial topology.

Ex. 3 Read and translate the following text

GEOMETRY AND TOPOLOGY

Geometry is the mathematical study of shapes and figures. There are many different kinds of shapes besides the familiar circles, triangles, and squares. This ancient branch of mathematics deals with points, lines, surfaces, and solids—and their relationships. Geometry explains how to build or draw shapes, measure them, compare them, and prove a number of different facts about them.

The geometry began when people felt the need to measure their lands while buying and selling. Its name is derived from Greek words meaning “Earth measurement.” “Geo” stands for earth and “metry” (metria) stands for measure.

Geometry was thoroughly organized in about 300 BC, when the Greek mathematician Euclid gathered what was known at the time, added original work of his own, and arranged 465 propositions into 13 books, collectively called ‘‘Elements’’. Geometry in ancient times was recognized as part of everyone's education. Early Greek philosophers asked that no one come to their schools who had not learned the ‘‘Elements’’ of Euclid. The books covered not only plane and solid geometry but also much of what is now known as algebra, trigonometry, and advanced arithmetic.

The oldest geometry is Euclidean geometry. Great mathematician Euclid is known as father of geometry. Euclidean geometry is the study of flat space. From the laws of Euclidean geometry, we get the famous theorem of Pythagoras, and all the formulas in trigonometry. In Euclidean geometry we also learned how to find the circumference and area of a circle.

In the 19th century, Euclidean geometry's status as the primary geometry was challenged by the discovery of non-Euclidean geometries. These inspired a new approach to the subject by presenting theorems in terms of axioms applied to properties assigned to undefined elements called points and lines. This led to many new geometries, including elliptical, hyperbolic, and parabolic geometries.

There are various branches of geometry like Analytic geometry, Projective geometry, Differential geometry, Non Euclidean geometry, Topology and geometry, Algebraic geometry. Modern abstract geometry deals with very general questions of space, shape, size, and other properties of figures. Projective geometry, for example, is an abstract geometry concerned with the geometric properties that remain invariant under the projection of figures onto other figures, as in the case of mathematical perspective.

A very useful approach to geometry is found in topology, the study of the properties of a geometric figure that remain the same when a figure is subjected to continuous transformation without loss of identity of any of its parts.

Topology may be roughly divided into point-set topology, which considers figures as sets of points having such properties as being open or closed, compact, connected, and so forth; combinatorial topology, which, in contrast to point-set topology, considers figures as combinations (complexes) of simple figures (simplexes) joined together in a regular manner; and algebraic topology, which makes extensive use of algebraic methods, particularly those of group theory.

Date: 2015-12-11; view: 979