What are octonions used for?
Octonions are related to exceptional structures in mathematics, among them the exceptional Lie groups. Octonions have applications in fields such as string theory, special relativity and quantum logic. Applying the Cayley–Dickson construction to the octonions produces the sedenions.
Are octonions Clifford algebra?
but the octonions are not a Clifford algebra, since they are nonassociative. Nonetheless, there is a profound relation between Clifford algebras and normed division algebras.
Who discovered octonions?
John Graves
John Graves, a lawyer friend of Hamilton’s, subsequently showed that pairs of quaternions make octonions: numbers that define coordinates in an abstract 8-D space. John Graves, the Irish lawyer and mathematician who discovered the octonions in 1843.
Why are octonions not associative?
The octonions are not associative Note that if any of the three corresponds to a real number, the order of the multiplication does not matter. If all the octonions correspond to quaternions, the order of multiplication will not matter, because the quaternions are associative.
What kind of math is physics?
Physics is often treated as an esoteric, challenging field, but much of physics is very basic, describing how things move in everyday life. You don’t have to be a mathematical genius to study physics, but you do need to know the basics, and college physics classes often use calculus and algebra.
Is Infinity an imaginary number?
Is infinity a imaginary number? No. Infinity is not a number.
What are the 8 dimensions in physics?
The most studied are the regular polytopes, of which there are only three in eight dimensions: the 8-simplex, 8-cube, and 8-orthoplex. A broader family are the uniform 8-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group.
Are quaternions vectors?
The vector part of a unit quaternion represents the radius of the 2-sphere corresponding to the axis of rotation, and its magnitude is the cosine of half the angle of rotation.
How do you write a quaternion?
A quaternion of the form a + 0 i + 0 j + 0 k, where a is a real number, is called scalar, and a quaternion of the form 0 + b i + c j + d k, where b, c, and d are real numbers, and at least one of b, c or d is nonzero, is called a vector quaternion.