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?
Quaternions are a mathematical concept that extends complex numbers to four dimensions. They are represented by four values: a real part and three imaginary parts.
Quaternions differ from complex numbers in that they have three imaginary parts instead of one, and they do not commute. This means that the order in which quaternions are multiplied matters.
Quaternions have many applications in computer graphics, robotics, and computer vision. They are often used for orientation and rotation calculations because they are more efficient than other methods.
Quaternions can represent rotations in three-dimensional space by using a unit quaternion, which has a magnitude of one. The rotation can be calculated by multiplying two quaternions together.
Yes, quaternions have applications in physics, particularly in quantum mechanics and electromagnetism. They are also used in mathematical models for particle dynamics and fluid mechanics.