Thursday, May 4, 2017

Is it possible to intuitively explain, how the three irrational numbers e, i and pi are related?




I read a bit about this equation: eiπ=1
For someone knowing high school maths this perplexes me. How are these three irrational numbers so seemingly smoothly related to one another? Can this be explained in a somewhat intuitive manner?
From my perspective it is hard to comprehend why these almost arbitrary looking irrational numbers have such a relationship to one another. I know the meanings and origins behind these constants.


Answer



Just think about it this way: π is related to the circle, whose equation is x2+y2=r2. Euler's constant e is related to the hyperbola, whose equation is x2y2=r2. In order to turn y2 into y2 we need a substitution of the form yiy.


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