Complex, Quaternions, Octonions, Sedenions
Each step from complex numbers to quaternions, octonions and sedenions loses an algebraic property, and the faces grow more anxious.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2024-01-01-complex-quaternions-octonions-sedenions/ (CC BY-NC 4.0)Transcript
ℂ complex numbers: associative ✓ commutative ✓ alternative ✓ [content] · ℍ quaternions: associative ✓ commutative ✗ alternative ✓ [uneasy] · 𝕆 octonions: associative ✗ commutative ✗ alternative ✓ [worried] · 𝕊 sedenions: associative ✗ commutative ✗ alternative ✗ [panicked]