This is called the most beautiful equation in mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner. Notice, however, its lack of rigor because it essentially depends on the above arbitrary definition for using the imaginary square root of -1 as an exponent, ''i.e.'', that <math>e^{i\phi} = \cos \phi + i\sin \phi \!</math>
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This is called the most beautiful equation in mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner.