Octonions

Octonions are an extension of the familiar numbers (like real numbers, complex numbers, and quaternions) used in advanced mathematics. While real numbers are one-dimensional and complex numbers are two-dimensional, octonions are eight-dimensional, meaning they involve eight components combined in a special way. They are non-commutative and non-associative, meaning the order of multiplication affects the result, and grouping doesn't always simplify calculations. Octonions are valuable in theoretical physics and mathematics, helping describe complex symmetries and higher-dimensional spaces that go beyond traditional number systems.