Difference between revisions of "Euler's Formula"
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(|||| seems to be accidental) |
(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.) |
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:<math>e^{i\pi} + 1 = 0 \!</math> | :<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. | + | 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. |
==See also== | ==See also== | ||
Revision as of 15:27, August 16, 2015
Euler's formula is the following identity in complex analysis making use of the imaginary number :
Euler's Identity
The formula can be used to derive an equation known as Euler's identity:
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.