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008			230418s2009 sz | s |||| 0|eng d
020			_a9783031023965
024	7		_a10.1007/978-3-031-02396-5 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA685 _b2009 EB
100	1		_aUngar, Abraham A. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9688135
245	1	2	_aA Gyrovector Space Approach to Hyperbolic Geometry _cby Abraham Ungar
250			_a1st edition 2009
264		1	_aCham _bSpringer International Publishing _c2009
300			_a1 recurso en línea (XII, 182 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Mathematics & Statistics _x1938-1751
505	0		_aGyrogroups -- Gyrocommutative Gyrogroups -- Gyrovector Spaces -- Gyrotrigonometry.
520			_aThe mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry.
988			_aSynthesis Collection of Technology_2009
650		7	_2embne _9138192 _aGeometría
776	0	8	_iPrinted edition: _z9783031012686
776	0	8	_iPrinted edition: _z9783031035241
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02396-5 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b04/2023 _dz _eIG _zSI