2010
DOI: 10.1007/978-90-481-8637-2
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Hyperbolic Triangle Centers

Abstract: this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. This book presents the novel approach to triangle centers in hyperbolic geometry that Einstein's special theory of r… Show more

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Cited by 22 publications
(7 citation statements)
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“…The definition of gyrogroups, some of which are gyrocommutative, is presented, for instance, in [3,4,7,8].…”
Section: Möbius Addition and Scalar Multiplicationmentioning
confidence: 99%
See 1 more Smart Citation
“…The definition of gyrogroups, some of which are gyrocommutative, is presented, for instance, in [3,4,7,8].…”
Section: Möbius Addition and Scalar Multiplicationmentioning
confidence: 99%
“…(1) Vector addition admits scalar multiplication, giving rise to vector spaces which, in turn, form the algebraic setting for analytic Euclidean geometry. In full analogy, (2) Einstein addition (of relativistically admissible velocities) admits scalar multiplication, giving rise to Einstein gyrovector spaces which, in turn, form the algebraic setting for the Klein ball model of analytic hyperbolic geometry [2][3][4][5][6][7]. Accordingly, the Klein model of hyperbolic geometry is also known as the relativistic model of hyperbolic geometry [8,9].…”
Section: Introductionmentioning
confidence: 99%
“…Φ 𝐻 𝑊 𝑈,𝑉 = 𝑊 𝑈,𝑉 Φ 𝑉 * 𝐻𝑈 (19) Its importance relies in the derivation of the formula that relates the action of the 𝐽-unitary group in terms of the three parameters (𝑈, 𝑉, 𝐻). Observe that…”
Section: The Matrix Blaschke Groupmentioning
confidence: 99%
“…i.e., gyrations represent rotations of the disc 𝔻 about its center. Thus, in terms of elementary translations and rotations the group structure of the hyperbolic transformations can be characterized by using the concept of the gyrogroups, that was introduced and applied mainly in the context of Einstein's special relativity, see, e.g., [20,19] and the references cited therein. The group operation, the Blaschke group, can be expressed as (𝑎, 𝛼) ⊙ (𝑏, 𝛽) = (𝑎 ⊕ 𝛼𝑏, gyr[𝑎, 𝛼𝑏]𝛼𝛽).…”
Section: Introductionmentioning
confidence: 99%
“…This view of a velocity-dependent mass is widespread in significant books, being adopted, among others, by Rindler [39,40], Sandin [34], Ungar [41] and Jammer [17]. On the opposite camp B, others side with the idea that mass is a relativistic invariant.…”
Section: E = MC 2 and Implications For Teachingmentioning
confidence: 99%