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007			cr nn 008mamaa
008			100623s2010 ne | s |||| 0|eng d
020			_a9789048186372 _9978-90-481-8637-2
040			_cMX-MeUAM
050		4	_aQC178
050		4	_aQC173.5-173.65
082	0	4	_a530.1 _223
100	1		_aUngar, A.A. _eauthor.
245	1	0	_aHyperbolic Triangle Centers _h[recurso electrónico] : _bThe Special Relativistic Approach / _cby A.A. Ungar.
264		1	_aDordrecht : _bSpringer Netherlands : _bImprint: Springer, _c2010.
300			_aXVI, 319p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aFundamental Theories of Physics ; _v166
505	0		_aThe Special Relativistic Approach To Hyperbolic Geometry -- Einstein Gyrogroups -- Einstein Gyrovector Spaces -- When Einstein Meets Minkowski -- Mathematical Tools For Hyperbolic Geometry -- Euclidean and Hyperbolic Barycentric Coordinates -- Gyrovectors -- Gyrotrigonometry -- Hyperbolic Triangle Centers -- Gyrotriangle Gyrocenters -- Gyrotriangle Exgyrocircles -- Gyrotriangle Gyrocevians -- Epilogue.
520			_aAfter A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein’s special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein’s relativistic mass hence meshes up extraordinarily well with Minkowski’s four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein’s special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology.
650		0	_aPhysics.
650		0	_aMathematics.
650		0	_aAstronomy.
650	1	4	_aPhysics.
650	2	4	_aClassical and Quantum Gravitation, Relativity Theory.
650	2	4	_aApplications of Mathematics.
650	2	4	_aTheoretical, Mathematical and Computational Physics.
650	2	4	_aAstronomy, Astrophysics and Cosmology.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9789048186365
830		0	_aFundamental Theories of Physics ; _v166
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-90-481-8637-2
596			_a19
942			_cLIBRO_ELEC
999			_c205673 _d205673