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This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography.
The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.

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Ruled surfaces.- Surfaces of revolution.- Translation surfaces.- Monge´s surfaces.- Continuous topographic and topographic surfaces.- Surfaces of congruent cross sections.- Continuous topographic and topographic surfaces.- Helical surfaces.- Spiral surfaces.- Spiral-shaped surfaces.- Helix-shaped surface.- One-sided surfaces.- Surfaces with spherical director curve.- Weingarten surfaces.- Surfaces of constant total curvature.- Surfaces of constant mean curvature.- Wave-shaped, waving, and corrugated surfaces.- Surfaces of umbrella type.- Kinematical surfaces of general type.- Second order surfaces.- Algebraic surfaces of high orders.- Quasi-polyhedra.- Equidistants of double systems.

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"The book under review is an encyclopedic publication about analytical and differential geometry of regular analytic surfaces, which found application in various branches of mathematics, engineering and construction. ... The book is intended for geometers, architects, builders and professionals dealing not only with geometry, but also people interested in fluid mechanics, optics and others. It will be useful to university teachers, school teachers, graduate students and students." (Ivailo Mladenov, zbMATH 1321.53001, 2015)

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Vyacheslav Ivanov and Sergey Krivoshapko are both Doctor of Technical Sciences, and Professor at Peoples´ Friendship University of Russia, Moscow.

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