Editing 179: e to the pi times i
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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. | The comic largely references {{w|Euler's identity}}. This identity states that e<sup>iπ</sup> + 1 = 0. Therefore, e<sup>iπ</sup> = −1. | ||
| − | 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]. | + | 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]. |
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). | 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). | ||
