Dictionary

octonion en · NOUN

Pronunciation

• /ɒkˈtəʊ.ni.ən/ (Received-Pronunciation)
• /ɑkˈtoʊ.ni.ən/ (General-American)

Etymology

Blend of Latin octō (“eight”) + quaternion.

Meanings

1. An 8-dimensional nonassociative extension of a quaternion with a real part and 7 imaginary parts (each a real multiple of a distinct square root of −1).
   • There is no theoretical limit to multispace dimensional numbering as there are definitions for octonion (8D), sedenion (16D), pathion (32D), chingon (64D), routon (128D), and voudon (256D) numbered space. 2023, Melanie Swan, Renato P. dos Santos, “Quantum Intelligence: Responsible Human-AI Entities”, in AAAI 2023 Spring Symposia, Socially Responsible AI for Wellbeing, March 27–29, 2023, USA, CEUR Workshop Proceedings, →DOI:
   • According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions (#92;mathbbO—Octonions) can be obtained, followed by 16D sedenions, 32D pathions, 64D chingons, 128D routons, and 256D voudons. 2022, Zlatka Valkova-Jarvis, Vladimir Poulkov, Viktor Stoynov, Dimitriya Mihaylova, Georgi Iliev, “A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks”, in Symmetry, volume 14, number 3, MDPI AG, →DOI, →ISSN:

Forms

Deriveds

octonionic · octonionics · octonionically

Hypernyms

hypercomplex number

Relateds

imaginary unit · quaternion · sedenion

Translations (8)

de Oktave (nonassociative extension of a quaternion) · fr octonion (nonassociative extension of a quaternion) · is áttundatala (nonassociative extension of a quaternion) · es octonión (nonassociative extension of a quaternion) · it ottonione (nonassociative extension of a quaternion) · ru октонио́н (nonassociative extension of a quaternion) · de Oktonion (nonassociative extension of a quaternion) · it ottetto (nonassociative extension of a quaternion)