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Titlebook: Hyperbolic Triangle Centers; The Special Relativi A.A. Ungar Book 2010 Springer Science+Business Media B.V. 2010 Application special relati

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发表于 2025-3-21 17:49:54 | 显示全部楼层 |阅读模式
书目名称Hyperbolic Triangle Centers
副标题The Special Relativi
编辑A.A. Ungar
视频video
概述Continuation of A. Ungar successful work on hyperbolic geometry, now with introduction of hyperbolic barycentric coordinates.Proves how, contrary to general belief, Einstein’s relativistic mass meshes
丛书名称Fundamental Theories of Physics
图书封面Titlebook: Hyperbolic Triangle Centers; The Special Relativi A.A. Ungar Book 2010 Springer Science+Business Media B.V. 2010 Application special relati
描述After 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 coord
出版日期Book 2010
关键词Application special relativity; Barycentric coordinates; Examining hyperbolic triangle center; Four-vec
版次1
doihttps://doi.org/10.1007/978-90-481-8637-2
isbn_softcover978-94-007-3265-0
isbn_ebook978-90-481-8637-2Series ISSN 0168-1222 Series E-ISSN 2365-6425
issn_series 0168-1222
copyrightSpringer Science+Business Media B.V. 2010
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发表于 2025-3-21 21:52:05 | 显示全部楼层
Gyrotriangle Gyrocentersgyrotriangle circumgyrocenter, ingyrocenter and orthogyrocenter, respectively. These gyrocenters are determined in this chapter in terms of their gyrobarycentric coordinate representations with respect to the vertices of their reference gyrotriangles.
发表于 2025-3-22 00:25:54 | 显示全部楼层
Book 2010 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
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When Einstein Meets Minkowskifour-vector formalism of Einstein’s special theory of relativity, along with its relevant consequences to the study of hyperbolic geometry in Part II and hyperbolic triangle centers in Part III of the book.
发表于 2025-3-22 17:59:08 | 显示全部楼层
Epilogueition law of hyperbolic geometry, which is commutative. This Epilogue of the book may thus serve as the Prologue for the future of Einstein’s special relativity theory as a theory regulated by the hyperbolic geometry of Bolyai and Lobachevsky.
发表于 2025-3-22 21:43:47 | 显示全部楼层
Euclidean and Hyperbolic Barycentric Coordinatesmechanics. Theorem 3.3 naturally suggests the introduction of the concept of barycentric coordinates into Euclidean geometry. Guided by analogies, we will see in this chapter how Theorem 3.2 naturally suggests the introduction of the concept of barycentric coordinates into hyperbolic geometry, where they are called gyrobarycentric coordinates.
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Gyrotriangle Gyroceviansat gyrocevians generate in gyrotriangles is presented. As an application, a special gyrocevian that generates special ingyrocircles is studied. Furthermore, gyrocevian concurrency conditions are uncovered and the hyperbolic version of the Theorem of Ceva is presented along with the related hyperbolic Brocard points.
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