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
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