Nice, interesting piece, especially the point about finance and its concept of debt leading to negative numbers. As opposed to geometry based numbers. Linked in turn to history of lending, usury and the concept of interest rates.
Working as a electrical engineer I'm quite used to exp rotating us around in the complex plane, though I never intuitively grasped why. The idea of when taking the derivative of exp(j), it always lands us back on the unit circle: seems so intuitive I'm surprised I didn't think of it myself. Thanks for the post, this was a fantastic read.
I really wish I'd seen this the first pass through calculus (I suffered through ODE 3 times before it suddenly became clear). Would have probably reduced my sentence to 2 passes total. On the other hand, PDE was suddenly easy for me, which helped when I went into numerical weather modeling!
Nice, interesting piece, especially the point about finance and its concept of debt leading to negative numbers. As opposed to geometry based numbers. Linked in turn to history of lending, usury and the concept of interest rates.
I vaguely remember remember doing this in A level maths from 1980 when we did cosh functions
Also, formula makes for great graffito! With perhaps a history?
Interesting... But, frankly, I looked it up, and [differentiation proof](https://en.wikipedia.org/wiki/Euler%27s_formula#Using_differentiation) feels better somehow :D
Working as a electrical engineer I'm quite used to exp rotating us around in the complex plane, though I never intuitively grasped why. The idea of when taking the derivative of exp(j), it always lands us back on the unit circle: seems so intuitive I'm surprised I didn't think of it myself. Thanks for the post, this was a fantastic read.
I think this video does a great job of explaining it also.
https://m.youtube.com/watch?v=FqHu-N5bGQo
I really wish I'd seen this the first pass through calculus (I suffered through ODE 3 times before it suddenly became clear). Would have probably reduced my sentence to 2 passes total. On the other hand, PDE was suddenly easy for me, which helped when I went into numerical weather modeling!