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A possible more general form of Euler's identity

 
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Oct22-12, 08:21 PM   #18
 
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A possible more general form of Euler's identity

https://fbcdn-sphotos-e-a.akamaihd.n...80170426_n.jpg
 
Oct22-12, 08:33 PM   #19
 
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i wander what they all look like superimposed on each other.

How many are there?

cos(x)/cos(1/y)=sin(1/x)/sin(y)
cos(x)/cos(1/y)=sin(y)/sin(1/x)
cos(x)/sin(1/x)=sin(y)/cos(1/y)
cos(x)/sin(1/x)=cos(1/y)/sin(y)
cos(x)/sin(y)=cos(1/y)/sin(1/x)
cos(x)/sin(y)=sin(1/x)/cos(1/y)
sin(y)/cos(x)=cos(1/y)/sin(1/x)
sin(y)/cos(x)=sin(1/x)/cos(1/y)

i make that 8
 
Oct22-12, 09:03 PM   #20
 
Quote by mapmatt View Post
i wander what they all look like superimposed on each other.

How many are there?

cos(x)/cos(1/y)=sin(1/x)/sin(y)
cos(x)/cos(1/y)=sin(y)/sin(1/x)
cos(x)/sin(1/x)=sin(y)/cos(1/y)
cos(x)/sin(1/x)=cos(1/y)/sin(y)
cos(x)/sin(y)=cos(1/y)/sin(1/x)
cos(x)/sin(y)=sin(1/x)/cos(1/y)
sin(y)/cos(x)=cos(1/y)/sin(1/x)
sin(y)/cos(x)=sin(1/x)/cos(1/y)

i make that 8
You're just taking combinations of sines and cosines. There's nothing special or unusual about this.
 
Oct22-12, 09:14 PM   #21
 
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Quote by Number Nine View Post
You're just taking combinations of sines and cosines. There's nothing special or unusual about this.
Almost correct, but also the sines and cosines or the reciprocals of x and y.

Can't you see anything special or unusual about the graphs they plot?
 
Oct22-12, 09:18 PM   #22
 
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I've still not seen them outside of the small plot given by wolframalpha.com

I'm going to try posting these on Wikipedia, along with each plot and the formulas written with no trig functions, just in terms of e, and i.

This time I might try posting to the talk page 1st, they might even let me put my starting function/expression up and keep it there!
 
Oct22-12, 09:33 PM   #23
 
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I suppose there'd be 24 with a z.
 
Oct22-12, 10:52 PM   #24
 
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Quote by Number Nine View Post
No, not for every possible value of (x, y). Not for x = 5 and y = 3.



Uh, why? What is that supposed to mean, exactly?



It's not a function, it's a relation. You've found a relation with a weird looking graph; there are lots of them.
It's only interesting if it means something, and you haven't demonstrated that this expression of yours means or does anything.
If you were to take these 'relations' as you call them to a high enough dimensions and look in the right place you might just find the universe.
 
Oct22-12, 10:55 PM   #25
 
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Quote by mapmatt View Post
If you were to take these 'relations' as you call them to a high enough dimensions and look in the right place you might just find the universe.
This thread has already degenerated into a conversation with yourself. I'm locking it.
 
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