Difference between revisions of "Euler's Formula"

Revision as of 18:35, August 17, 2015

Euler's formula is the following identity in complex analysis making use of the imaginary number $i$ :

e^{i\phi }=\cos \phi +i\sin \phi \!

Euler's Identity

The formula can be used to derive an equation known as Euler's identity:

e^{i\pi }+1=0\!

This is called the most beautiful equation in mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner.

@@ Line 8: / Line 8: @@
 :<math>e^{i\pi} + 1 = 0 \!</math>
-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>
+This is called the most beautiful equation in mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner.
 ==See also==

Difference between revisions of "Euler's Formula"

Revision as of 18:35, August 17, 2015

Euler's Identity

See also

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