Fantastic Quaternions - Numberphile
Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY More links & stuff in full description below ↓↓↓...
==========
How do you rotate an object in three dimensions? So, you take an object like that,and rotate it. That would be something that's useful, you can imagine, in computergraphics. But how are we gonna do this? Now, one of the neatest ways of doing thismathematically uses a new type of number, beyond the regular numbers you know.So this is beyond the real numbers, as we call them.They're even beyond the complex numbers—if you've heard of complex numbers before—it is evenbeyond that. They are called quaternions. They are fantastic! So imagine that I want to movealong in one dimension. So you are living somewhere here and if I said move +5.+5 means that you move 5 units to the right along this line, so I'd end up over here.If I said instea...
==========
How do you rotate an object in three dimensions? So, you take an object like that,and rotate it. That would be something that's useful, you can imagine, in computergraphics. But how are we gonna do this? Now, one of the neatest ways of doing thismathematically uses a new type of number, beyond the regular numbers you know.So this is beyond the real numbers, as we call them.They're even beyond the complex numbers—if you've heard of complex numbers before—it is evenbeyond that. They are called quaternions. They are fantastic! So imagine that I want to movealong in one dimension. So you are living somewhere here and if I said move +5.+5 means that you move 5 units to the right along this line, so I'd end up over here.If I said instea...
