Octonions example sentences

Related (4): quaternions, algebra, non-associative, automorphism.

"Octonions" Example Sentences

1. "Octonions" are a type of algebraic structure that can be used to represent rotations in three-dimensional space.
2. It is believed that "octonions" may be useful in physics and quantum mechanics.
3. "Octonions" are also known as Cayley numbers or Cayley-Dickson algebras.
4. The "octonions" form a non-associative algebra with eight dimensions.
5. "Octonions" are related to the quaternions, which were first discovered by Sir William Rowan Hamilton in 1843.
6. "Octonions" are the largest of the four division algebras, which also include the real numbers, complex numbers, and quaternions.
7. "Octonions" are not commutative, meaning that the order of multiplication matters.
8. "Octonions" have been studied extensively by mathematicians, but their applications remain largely unknown.
9. "Octonions" are related to the Lie groups, which are used to describe symmetries in physics.
10. "Octonions" can be used to construct a variety of mathematical objects, such as spinors and projective spaces.
11. "Octonions" have a unique property known as the octonionic identity, which states that the product of any two octonions is equal to the sum of their squares.
12. "Octonions" are related to the concept of Clifford algebras, which are used to describe the geometry of space-time.
13. "Octonions" can be used to construct a variety of higher-dimensional geometries, such as the Minkowski space-time.
14. "Octonions" are related to the concept of Clifford algebras, which are used to describe the geometry of space-time.
15. "Octonions" are related to the concept of projective geometry, which is used to describe curved surfaces in three-dimensional space.
16. "Octonions" have been used to construct a variety of higher-dimensional geometries, such as the octonionic projective space.
17. "Octonions" are related to the concept of Lie algebras, which are used to describe symmetries in physics.
18. "Octonions" can be used to construct a variety of mathematical objects, such as spinors and projective spaces.
19. "Octonions" have a unique property known as the octonionic identity, which states that the product of any two octonions is equal to the sum of their squares.
20. "Octonions" are related to the concept of Clifford algebras, which are used to describe the geometry of space-time.
21. "Octonions" can be used to construct a variety of higher-dimensional geometries, such as the Minkowski space-time.
22. "Octonions" are related to the concept of projective geometry, which is used to describe curved surfaces in three-dimensional space.
23. "Octonions" have been used to construct a variety of higher-dimensional geometries, such as the octonionic projective space.
24. "Octonions" are related to the concept of Lie algebras, which are used to describe symmetries in physics.
25. "Octonions" have been used in a variety of mathematical applications, such as quantum computing, cryptography, and robotics.
26. "Octonions" have been studied extensively by mathematicians, but their applications remain largely unknown.
27. "Octonions" are related to the quaternions, which were first discovered by Sir William Rowan Hamilton in 1843.
28. "Octonions" are the largest of the four division algebras, which also include the real numbers, complex numbers, and quaternions.
29. "Octonions" form a non-associative algebra with eight dimensions.
30. "Octonions" are not commutative, meaning that the order of multiplication matters.
31. "Octonions" have been used to develop a variety of mathematical models, such as quantum field theory and string theory.
32. "Octonions" can be used to construct a variety of mathematical objects, such as spinors and projective spaces.
33. "Octonions" are related to the concept of Clifford algebras, which are used to describe the geometry of space-time.
34. "Octonions" have a unique property known as the octonionic identity, which states that the product of any two octonions is equal to the sum of their squares.
35. "Octonions" are related to the concept of projective geometry, which is used to describe curved surfaces in three-dimensional space.
36. "Octonions" have been used to construct a variety of higher-dimensional geometries, such as the octonionic projective space.
37. "Octonions" are related to the concept of Lie algebras, which are used to describe symmetries in physics.
38. "Octonions" have been used to develop a variety of mathematical models, such as quantum field theory and string theory.
39. "Octonions" are believed to be useful in physics and quantum mechanics.
40. "Octonions" are a type of algebraic structure that can be used to represent rotations in three-dimensional space.