| Description |
Quaternions are often introduced as an extension of the complex numbers, but this choice is arbitrary. This thesis explores the world of quaternions, H, and their application without the language or context of complex numbers. This choice has the benefit of preventing intuitions that work in C from improperly being associated to quaternions. We will explore the way in which quaternions are used in efficient calculations involving rotations in R3. Finally, we will define the complex numbers as any of infinitely many equivelent subrings of the quaternions and show this definition is equivalent to standard definitions of C. Then we will prove Euler's theorem under the lens of quaternions to emphasize the equivalence and additional insight provided by quaternions on complex numbers. |
