Comment on Understanding the most beautiful equation in MathematicsComments−cmvkk13yHere's my favorite explanation of this formula:http://betterexplained.com/articles/intuitive-understanding-...−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 =).
Comments
Here's my favorite explanation of this formula:
http://betterexplained.com/articles/intuitive-understanding-...
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 =).