In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors. Interested about Quaternions & rotations go here to learn more..
1. hamilton walk
On October 16th in the year 1843, Sir William Rowan Hamilton departed from his residence at Dunsink Observatory on a walk into Dublin. On this walk, Hamilton had a sudden moment of insight at the site of Broom Bridge which led to his invention of a new breed of numbers called quaternions. This walk has become significant to mathematicians, many of whom treat it as a mathematical pilgrimage. This video is my homage to the Hamilton Walk.
2. william rowan
hamilton
Nice! Youtubers! Lin-Manuel Miranda would be proud.
3. quaternions:
If you are confused by the equation i^2 = j^2 = k^2 = ijk = -1 , go to the next video. The reason it looks so weird is because you lose the commutative property when you go from 2D rotation to 3D rotation, the property stating that ab = ba .
This means that the order of multiplication matters, and that if you reorder them, you get a different result.
4. Stereographic
projection
One thing that makes quaternions so challenging is that they live and act in four dimensions, which is extremely hard (impossible?) to visualize. Luckily, we can build an intuition for quaternion multiplication and how it computes rotation in 3d just by focusing on unit quaternions, the ones which sit a distance 1 from the origin. https://eater.net/quaternions
No points for noticing the wall decor at the start :
" Les Aventures de Tintin " "Objectif Lune"
The Adventures of Tintin ( Destination Moon )
- By Hergé
1 of 6: Aaron a you-tuber sharing his amazing 'hamilton walk'