Explain xkcd: It's 'cause you're dumb.
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| − | {{comic
| + | my balls |
| − | | number = 179
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| − | | date = November 3, 2006
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| − | | title = e to the pi times i
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| − | | image = e_to_the_pi_times_i.png
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| − | | titletext = I have never been totally satisfied by the explanations for why e to the ix gives a sinusoidal wave.
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| − | }}
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| − | ==Explanation==
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| − | The comic largely references {{w|Euler's identity}}. This identity states that e<sup>iπ</sup> + 1 = 0. Therefore, e<sup>iπ</sup> = −1.
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| − | The humor from this comic is because of the seemingly arbitrary relationship between e, π, and the identity of i (the square root of −1). e is the mathematical identity of which the derivative of e<sup>x</sup> with respect to x is still e<sup>x</sup>, while π is the relationship between the circumference of a circle divided by its diameter. Taking these two values and applying them to the value of i in such a manner makes it seem counter-intuitive that it would yield −1 from basic analysis. The above linked Wikipedia page goes into good detail of how to derive this identity, as does [https://www.youtube.com/watch?v=-dhHrg-KbJ0 this YouTube video].
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| − | The title text refers to how Euler's identity is called upon in complex form (separating real and imaginary numbers): e<sup>ix</sup> = cos(x) + i sin(x).
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| − | ==Transcript==
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| − | :[Two Cueballs are standing at a board with writing on. One Cueball is pointing at the board.]
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| − | :Cueball: Numbers of the form n√-1 are "imaginary," but can still be used in equations.
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| − | :Friend: Okay.
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| − | :Cueball: And e^(π√-1)=-1.
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| − | :Friend: Now you're just fucking with me.
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| − | {{comic discussion}}
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| − | [[Category:Comics featuring Cueball]]
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| − | [[Category:Math]]
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Revision as of 01:27, 5 May 2022
