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Improvements in wording and notation. (#27370)

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Andrew Mackie
2019-05-16 22:54:15 -07:00
committed by Parth Parth
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guide/english/mathematics/eulers-formula/index.md
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--- ---
title: Eulers Formula title: Eulers Formula
--- ---
## Eulers Formula ## Euler's Formula
Eulers Formula is a mathematical identity which states that (for any value of x): Euler's Formula is a mathematical identity which states that, for any value of <em>x</em> (and where <em>e</em> is the base of the natural logarithm and <em>i</em> is the square root of -1):
e^(ix)=cosx+isinx
This is of interest because of the following case:
When x=pi, Euler's Formula gives the beautiful identity invovling pi, e, and i.
e^(ipi)+1=0, <em>e</em><sup><em>ix</em></sup> = cos <em>x</em> + <em>i</em> sin <em>x</em>
A famous joke for mathematicians is "How many mathematicians does it take to change a light bulb?" and answers "-e^(ipi)" Furthermore, when <em>x</em> = <em>&pi;</em>, Euler's Formula results in the following beautiful identity relating <em>&pi;</em>, <em>e</em>, and <em>i:</em>
<em>e</em><sup><em>i&pi;</em></sup> + 1 = 0
A famous joke for mathematicians answers the question "How many mathematicians does it take to change a light bulb?" with "<em>-e</em><sup><em>i&pi;</em></sup>".
Can you tell what the answer is? Can you tell what the answer is?
This is often used when dealing with complex numbers in exponential form. This is often used when dealing with complex numbers in exponential form.