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diff --git a/themes/emily_zola_theme/content/post/mathjax_support.md b/themes/emily_zola_theme/content/post/mathjax_support.md deleted file mode 100644 index 709d27c..0000000 --- a/themes/emily_zola_theme/content/post/mathjax_support.md +++ /dev/null @@ -1,30 +0,0 @@ -+++ -title = "MathJax Support" -date = 2021-01-03 -[taxonomies] -categories = ["math"] -tags = ["Euler's identity"] -[extra] -math = true -+++ - -**Please add the following lines in the front matter when using MathJax.** - -``` -[extra] -math = true -``` - ---- - -#### Euler's identity - -$e^{i\pi }+1=0$ - -#### Geometric interpretation - -Any complex number $z=x+iy$ can be represented by the point $(x,y)$ on the complex plane. This point can also be represented in polar coordinates as $(r,\theta )$, where $r$ is the absolute value of $z$ (distance from the origin), and $\theta$ is the argument of $z$ (angle counterclockwise from the positive x-axis). By the definitions of sine and cosine, this point has cartesian coordinates of $(r\cos \theta ,r\sin \theta )$, implying that $z=r(\cos \theta +i\sin \theta )$. According to Euler's formula, this is equivalent to saying $z=re^{i\theta}$. - -Euler's identity says that $-1=e^{i\pi }$. Since $e^{i\pi }$ is $re^{i\theta }$ for $r$ = 1 and $\theta =\pi$ , this can be interpreted as a fact about the number −1 on the complex plane: its distance from the origin is 1, and its angle from the positive x-axis is $\pi$ radians. - -[Euler's identity \- Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity)
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