The discussion revolves around quaternions, exploring their definition, mathematical properties, and applications, particularly in computer graphics. Participants seek to understand quaternions in simpler terms and their significance compared to complex numbers and matrix representations.
Participants generally agree on the utility of quaternions in computer graphics and their mathematical properties, but there remains uncertainty regarding their historical development and the reasons for their necessity as an extension of complex numbers.
Some limitations in understanding the historical context of quaternions and their comparison to vector analysis are noted, as well as the unresolved nature of why complex numbers were deemed insufficient.
wikipedia said:From the mid 1880s, quaternions began to be displaced by vector analysis, which had been developed by Josiah Willard Gibbs and Oliver Heaviside. Vector analysis described the same phenomena as quaternions, so it borrowed ideas and terms liberally from the classical quaternion literature. However, vector analysis was conceptually simpler and notationally cleaner, and eventually quaternions were relegated to a minor role in mathematics and physics.
However, quaternions have had a revival in the late 20th century, primarily due to their utility in describing spatial rotations. Representations of rotations by quaternions are more compact and faster to compute than representations by matrices...
JungleJesus said:I've seen quaternions mentioned in a few articles online and I think they could be a very interesting subject. I would like to learn about them in simpler terms first. Can anyone give me the rundown on what they are and how they work?