Editing 179: e to the pi times i
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{{comic | {{comic | ||
+ | | horizontal = yes | ||
| number = 179 | | number = 179 | ||
| date = November 3, 2006 | | date = November 3, 2006 | ||
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| image = e_to_the_pi_times_i.png | | image = e_to_the_pi_times_i.png | ||
| titletext = I have never been totally satisfied by the explanations for why e to the ix gives a sinusoidal wave. | | titletext = I have never been totally satisfied by the explanations for why e to the ix gives a sinusoidal wave. | ||
+ | | imagesize = | ||
}} | }} | ||
==Explanation== | ==Explanation== | ||
− | The comic largely references {{w|Euler's identity}}. This identity states that e | + | The comic largely references {{w|Euler's identity}}. This identity states that e^(i*π) + 1 = 0. Therefore, e^(i*π) = -1. |
− | The | + | The humour from this comic is because of the seemingly arbitraty 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^x with respect to x is still e^x, while π is the relationship between the circumfrance of a circle divided by its diameter. Taking these two values and applying them to the value of i in such a manner seems counterintuitive to getting i^2 (-1) from basic analysis. The above linked Wikipedia page goes into good detail of how to derive this identity. |
− | The title text refers to how Euler's identity is called upon in complex form (separating real and imaginary numbers): e | + | The title text refers to how Euler's identity is called upon in complex form (separating real and imaginary numbers): e^(i*x) = cos(x) + i*sin(x). |
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