Nenad said:
Dominguez Scaramanga said:looks like it can be implimented in quantum physics... have a look here, it's all way over my head and I didnt read much of it, but they're certainly using quaternions!
marlon said:
Quaternions and octonions are mathematical concepts that extend the idea of complex numbers. They involve a combination of real and imaginary numbers and are used to represent rotations in three and four-dimensional space, respectively.
Quaternions and octonions have many practical applications in fields such as mechanics, physics, computer graphics, and robotics. They are used to represent rotations and orientations in 3D and 4D spaces, making them useful in computer animation and game development. They are also used in quantum mechanics to describe the properties of particles.
Quaternions and octonions differ from complex numbers in several ways. Unlike complex numbers, which have two imaginary units (i and -i), quaternions have three imaginary units (i, j, and k), and octonions have seven imaginary units. Also, while complex numbers can be commutative, quaternions and octonions are non-commutative, meaning the order in which they are multiplied matters.
Yes, quaternions and octonions can be visualized using a geometric representation called the "Cayley-Dickson construction." This involves plotting the real and imaginary components of the numbers on different axes, similar to how complex numbers can be plotted on a 2D plane.
While quaternions and octonions may seem complex at first, they can be understood with a basic understanding of algebra and geometry. With practice and familiarity, they can become useful tools in various fields of mathematics and science.