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I never forget the moment when my math teacher revealed e^pi*i+1=0 after dealing with complex numbers. It was beautiful.

• gizmo686 13y ago
  I think I am unique in being one of the only people whose first reaction to seeing that equation was to think that it was a mistake (in fact, my first reaction to seeing it is still to think it is a mistake, even knowing that it is not). To me, it feels like the plus sign should be a minus sign, to give the (incorrect) equation `e^pi * i-1=0`. Years after I saw the equation, when I learned how it actually made sense to talk about complex exponents, I realized that the problem is that pi is a stupid constant, but that is another discussion. Returning to the `e^pi * i+1=0` point, I still don't get why people find that beautiful before they have any sense of what taking a complex exponent means (in terms of how to naturally extend the definition of exponent, obviously the geometric result essentially follows from this result). More to the point, that equation is just a special case of Euler's formula, `e^xi=cos(x) + i * sin(x)`, which is what contains the real beautiful insight. EDIT: fixed * formatting
  • jimmaswell 13y ago
    The part of it that people find cool is probably e, i, and pi being related, when at first you wouldn't think they had anything to do with each other, before knowing any of that.