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## A possible more general form of Euler's identity

 Recognitions: Gold Member 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

 Quote by mapmatt 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

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 Quote by Number Nine 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?

 Recognitions: Gold Member 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!
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 Quote by Number Nine 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.

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