University of Kashan Mathematics Interdisciplinary Research 2538-3639 1 1 2016 01 01 The Intrinsic Beauty, Harmony and Interdisciplinarity in Einstein Velocity Addition Law: Gyrogroups and Gyrovector Spaces 5 51 13636 10.22052/mir.2016.13636 EN Abraham A. Ungar North Dakota State University Journal Article 2016 01 22 The only justification for the Einstein velocity addition law ‎appeared to be its empirical adequacy‎, ‎so that the ‎intrinsic beauty and harmony in Einstein addition remained for a long time ‎a mystery to be conquered‎. ‎Accordingly‎, ‎the aim of this expository article is to present ‎(i) the Einstein relativistic vector addition‎, ‎(ii) the resulting Einstein scalar multiplication‎, ‎(iii) the Einstein relativistic mass‎, ‎and ‎(iv) the Einstein relativistic kinetic energy‎, ‎along with remarkable analogies with classical results in ‎groups and vector spaces that these ‎Einstein concepts capture in gyrogroups and gyrovector spaces‎. ‎Making the unfamiliar familiar‎, ‎these analogies uncover the ‎intrinsic beauty and harmony in the underlying ‎Einstein velocity addition law of relativistically admissible velocities‎, ‎as well as its interdisciplinarity‎. https://mir.kashanu.ac.ir/article_13636_01f4395f33b5311416ea86da2a1e38d4.pdf