Ask AI: What are some practical applications of octonions?

1. Octonions can be used to solve certain problems in robotics, such as the inverse kinematics of robotic arms, by exploiting the algebraic structure of their composition. 2. They can be used to give a theoretical framework for differential geometry, which can be used to explain geometric principles in higher dimensions. 3. Octonions can be used to describe certain subatomic particles in quantum mechanics, such as quarks and leptons. 4. Octonions have been used in some advanced machine learning and artificial intelligence algorithms, such as U-nets. 5. They can be used to represent the rotation group in four dimensions, which is relevant in the study of relativity. 6. Octonions have found application in the study of group theory and abstract algebra.