8 ms·
For anyone that finds it beautiful isn't there a bit of humanisation and definition involved (for example the Sine function used in deriviation uses 'pi' instea
by neximo64 10y ago
For anyone that finds it beautiful isn't there a bit of humanisation and definition involved (for example the Sine function used in deriviation uses 'pi' instead of 90 degrees), not to mention Sine is a human created function. You could have e to pi (90 * -1) too.. or a different method to define angles instead of having 360 degrees (base 60)
- panic 10y agoYeah, you can have the same thing with degrees if you use a different exponent base than e: e^((pi/180)ix) = (e^(pi/180))^ix = E^ix and therefore E^180i = -1 where E is about 1.0176065. The particular base e has some nice properties, though, like that its rate of change d/dx e^ix at a given point x is just i e^ix. The rage of change for E^ix, on the other hand, is d/dx E^ix = (pi/180) i E^ix, which is a little less "natural". This strange fact -- that using radians makes the expression e^ix = cos x + i sin x have a nice derivative -- is one of the reasons why mathematicians like to define these functions in terms of radians instead of degrees.
- deleted 10y ago[deleted]
- bbcbasic 10y agoSurvivorship bias of beautiful math. Who want's to study systems that don't simply and compose well. The exception that proves the rule is the 4 color theorem - ugly big-arse proof generated by a machine. Who is going to look into that any further?