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Geometry. Textbook. (Geometriya. Uchebnoe posobie.) (Russian) Zbl 0727.51001

Moskva: Nauka. 672 p. R. 1.50 (1990).
The book has been written for students of pedagogical institutes. It contains a school version of geometry, completed by some university lectures on geometry, differential geometry and topology.
The particular chapters deal with different geometrical branches. The first chapter contains a background of the analytical geometry. It starts with the definiton of the system of coordinates and contains all the standard facts about straight lines, planes, curves and surfaces of second degree. The second chapter (called “The elementary geometry”) is devoted to an axiomatic description of Euclidean geometry based on the primitive notions: “the point” and “the segment”.
Some transformations and corresponding to them geometries are considered in the third chapter. Isometries as well as similarities and inversions, affine and projective transformations are discussed there. An axiomatization of n-dimensional Euclidean geometry, based on the notions “point”, “segment” and “space” is presented there too.
The fourth chapter is concerned with differential geometry; it describes the theory of curves and surfaces in \({\mathbb{R}}^ 3\). The authors deal with Frenet formulas, natural equations of curves, the first and second quadratic forms as well as geodesic lines.
In the fifth chapter a background of general topology is given. The analysis is concluded with the classification of compact surfaces.
The sixth chapter is concerned with foundations of geometry. The Euclidean geometry with axioms of congruence of segments and continuity is discussed and some information on the theory of models is given.

MSC:

51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
51M04 Elementary problems in Euclidean geometries
51Nxx Analytic and descriptive geometry
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