Every Hypercomplex Number Explained
What happens when you go beyond complex numbers? This video explores some of the strangest and most fascinating number systems mathematicians have discovered.
Chapters:
00:00 Complex numbers
01:30 Quaternions
02:43 Cayley-Dickson construction
03:47 Split-complex numbers
06:03 Multicomplex numbers
08:18 Modified Cayley-Dickson construction
10:25 Dual numbers
12:28 Generalized complex numbers
15:03 Clifford algebras
17:30 Quotient rings
#SoME4
Further research:
An algorithm for multiplication of trigintaduonions, Alexandr Cariow & Galina Cariowa
James Cockle (1848) On a New Imaginary in Algebra, Philosophical Magazine 33:438
The Multicomplex Numbers and Their Properties on Some Elementary Functions, Md. Nasiruzzamanand M. Mursaleen
Matrix Theory Over the Split Quaternions, MEHDI JAFARI and YUSUF YAYLI
De-Moivre and Euler Formulae for Dual-Complex Numbers, Mehmet Ali Gung and Omer Tetik
Geometry of Generalized Complex Numbers, ANTHONY A. HARKIN & JOSEPH B. HARKIN
Clifford algebras and Bott Periodicity: https:// demonstrations.wolfram.com/TrigramsAndRealCliffordAlgebras/
Complex numbers: • Imaginary Numbers Are Real [Part 1: Introd...
Quaternions: • Visualizing the 4d numbers Quaternions
Cayley-Dickson construction: • Climbing past the complex numbers.
Split-complex numbers: • Unsolvable Equation? | Split-Complex Numbers
Split-octonions: • The strange utility of this mutant matrix.
Dual numbers: • Unsolvable System of Equations? | Dual Num...
Generalized complex numbers: • The complex number family.
Clifford algebras: • Clifford Algebras and Time Loops
No 3d complex numbers: • Why are there no 3 dimensional "complex nu... and • Why are there no 3 dimensional "complex nu...
Quotient rings: • Number Systems Invented to Solve the Harde...
Other stuff:
https://www. reddit.com/r/mathmemes/comments/ogol4l/keep_going_higher/
https://www. reddit.com/r/mathmemes/comments/1cfwetu/number_systems_be_like/
https://www. reddit.com/r/mathmemes/comments/180rwdw/whats_a_number/
https://www. reddit.com/r/math/comments/9urjyx/why_there_is_no_complex_numbers_in_3_dimension/
https://www. quora.com/Why-are-there-no-3D-complex-numbers
On this page of the site you can watch the video online Every Hypercomplex Number Explained with a duration of hours minute second in good quality, which was uploaded by the user Johttacus J. J. Begallo 01 June 2025, share the link with friends and acquaintances, this video has already been watched 141,270 times on youtube and it was liked by 5.8 thousand viewers. Enjoy your viewing!
