TY - JOUR
T1 - Elementary Derivations of the Euclidean Hurwitz Algebras Adapted from Gadi Moran’s last paper
AU - Moran, Tomer
AU - Moran, Shay
AU - Moran, Shlomo
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2021/9/14
Y1 - 2021/9/14
N2 - “Real Normed Algebras Revisited,” the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their properties, using only what was known to 19th-century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above-mentioned classical results using only basic properties of the geometry of Euclidean spaces and tools from high school geometry. His reconstructions underline an interesting connection between Euclidean geometry and these algebras, and avoid the advanced machinery used in previous derivations of these results. The goal of this article is to present Gadi’s derivations in a way that is accessible to a wide audience of readers.
AB - “Real Normed Algebras Revisited,” the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their properties, using only what was known to 19th-century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above-mentioned classical results using only basic properties of the geometry of Euclidean spaces and tools from high school geometry. His reconstructions underline an interesting connection between Euclidean geometry and these algebras, and avoid the advanced machinery used in previous derivations of these results. The goal of this article is to present Gadi’s derivations in a way that is accessible to a wide audience of readers.
KW - MSC
UR - http://www.scopus.com/inward/record.url?scp=85115642350&partnerID=8YFLogxK
U2 - 10.1080/00029890.2021.1949219
DO - 10.1080/00029890.2021.1949219
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AN - SCOPUS:85115642350
SN - 0002-9890
VL - 128
SP - 726
EP - 736
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 8
M1 - 8
ER -