mistercrayon wrote:I find the identity a bit of a swizzy cheat.
Firstly because the 0 is shoehorned in there by rearrangement.
Secondly couldn't the pi be replaced by any number if you chose the appropriate number of degrees in a circle? Say if a full rotation equalled 4 then it would be e^2i = -1?
SpaceGazelle wrote:Besides being wrong, you're missing the point.mistercrayon wrote:I find the identity a bit of a swizzy cheat. Firstly because the 0 is shoehorned in there by rearrangement. Secondly couldn't the pi be replaced by any number if you chose the appropriate number of degrees in a circle? Say if a full rotation equalled 4 then it would be e^2i = -1?
acemuzzy wrote:And yeah, e and i are equally not-chosen-at-random. e has the magic property that if you draw the graph y=e^x, the angle of the line at any point precisely matches the value y value. No other number has that property. (Well, except 0 I guess .)
Its stuff like this that really got me interested in maths and physics before I ran up against the limits of my own limited facility with them and my lack of patience for undertaking the hard graft in learning that would provide any real understanding.SpaceGazelle wrote:I did all this in the Maroon Room about this exact equation. On phone so I'll be brief.
It tells us that there is a direct relationship between several fundamental constants, and that imaginary numbers are part of that relationship, and that relationship is true and proved in the tightest sense. It tells us there is perhaps a deeper truth of why these constants might be related, and that truth connects constants and mathematics im ways not understood. It hints that reality is made of mathematics, not described by it.
mistercrayon wrote:acemuzzy wrote:And yeah, e and i are equally not-chosen-at-random. e has the magic property that if you draw the graph y=e^x, the angle of the line at any point precisely matches the value y value. No other number has that property. (Well, except 0 I guess .)
I think there must have been a number with this property. The fact we find that property interesting is surely how you end up finding e.
SpaceGazelle wrote:On phone so no links. Not sure if there are links tbh. There are no particles and there are no waves, there is only equations and constants
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