Comment on Understanding the most beautiful equation in MathematicsparentComments−a-nikolaev13yMy favorite:1) Using Taylor Series, show that exp(ix)=cos(x)+i*sin(x).2) Then the result is trivial for x=piThis image helps:https://en.wikipedia.org/wiki/File:Euler%27s_formula.svg−stephencanon13yTaylor series are ugly; do it directly from the definition of the functions as solutions to specific differential equations =).
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My favorite:
1) Using Taylor Series, show that exp(ix)=cos(x)+i*sin(x).
2) Then the result is trivial for x=pi
This image helps:
https://en.wikipedia.org/wiki/File:Euler%27s_formula.svg
Taylor series are ugly; do it directly from the definition of the functions as solutions to specific differential equations =).