## To Be Improved Normal Curve

### First function plot with pattern fill

Adaptations for standalone documents:

• \usetikzlibrary{pattern} before \begin{document}
• \pgfplotsset{compat=1.6}
\begin{tikzpicture}
\begin{axis} [axis lines=center,legend style={at={(0.7,0.7)},anchor=south west}]
\addplot [domain=-3:3, thick, smooth, yellow] { 1/sqrt(2*pi)*exp(-x^2/2) };
\addlegendentry{$y = \tfrac{1}{\sqrt{2\pi}} e^{-x^2/2}$};
\addplot [dashed, yellow] coordinates {(1.5,0) (1.5,0.14)};
\addplot[domain=-3:1.5, pattern=north east lines,draw=none, fill opacity=0.3]
{ 1/sqrt(2*pi)*exp(-x^2/2) } \closedcycle;
\end{axis}
\end{tikzpicture}


## Trigonometric Functions by Unit Circle

For secondary school students, I define cosine and sine as the x and y-components of the point A (cos θ, sin θ) on the unit circle x² + y² = 1, and the tangent function as the quotient of sine over cosine. \begin{tikzpicture}[scale=3] \coordinate (O) at (0,0); \coordinate (H) at (0.6,0); \coordinate (A) at (0.6,0.8); \coordinate (E) at (1,0); \coordinate (T) at (1,0.8/0.6); \draw (O) circle (1); \draw[->] (-1.3,0) -- (1. [Read More]

## Matrix Diagonalisation and Change of Basis

Here’s the $\LaTeX$ code of my diagram for matrix diagonalisation to be used on Discord. Why do matrix diagonalisation on square matrix $P$? If we can find a diagonal matrix $D$ and a square matrix $Q$ such that $P = QDQ^{-1}$, then we can easily compute $(P + \lambda I)^n$ for any scalar $\lambda$ and integer $n$ because $D^n$ is easy to compute. $\begin{tikzcd} {{}} & {{}} & \cdots& {} \\{{}} & {{}} & \cdots& {{}} \arrow["P", from=1-1, to=1-2]\arrow["{Q^{-1}}"', from=1-1, to=2-1]\arrow["D"', from=2-1, to=2-2]\arrow["Q"', from=2-2, to=1-2]\arrow["P", from=1-2, to=1-3]\arrow["D"', from=2-2, to=2-3]\arrow["P", from=1-3, to=1-4]\arrow["D"', from=2-3, to=2-4]\arrow["Q"', from=2-4, to=1-4]\end{tikzcd}$ After viewing the power of the Discord bot $\TeX{}$it, which renders $\LaTeX$ code on Discord, I gave up spending more time on exploring more functionalities of $\KaTeX$ (say, commutative diagrams) because Discord and $\LaTeX$ spread math knowledge much better than a static blog for basic math: the former allows instant feedback from the reader. [Read More]

## LaTeX Code for Linear System

\begin{align} A\mathbf{x} &= \mathbf{b} \\ \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} &= \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix} \\ \begin{bmatrix} \vert & \vert & \vert \\ \mathbf{a}_1 & \mathbf{a}_2 & \mathbf{a}_3 \\ \vert & \vert & \vert \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} &= \mathbf{b} \\ x_1 \mathbf{a}_1 + x_2 \mathbf{a}_2 + x_3 \mathbf{a}_3 &= \mathbf{b} \tag{$\star$} \\ \begin{pmatrix} a_{11} x_1 + a_{12} x_2 + a_{13} x_3 \\ a_{21} x_1 + a_{22} x_2 + a_{23} x_3 \\ a_{31} x_1 + a_{32} x_2 + a_{33} x_3 \end{pmatrix} &= \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix} \\ x_1 \begin{pmatrix} a_{11} \\ a_{21} \\ a_{31} \end{pmatrix} + x_2 \begin{pmatrix} a_{12} \\ a_{22} \\ a_{32} \end{pmatrix} + x_3 \begin{pmatrix} a_{13} \\ a_{32} \\ a_{33} \end{pmatrix} &= \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix} \end{align} Source code: [Read More]

## Ways to Draw Diagrams Displayed on Math.SE

I wanted to start a meta question, but I don’t see a point of that after viewing some related posts listed at the end of the next subsection. Intended question You may vote on your preferred way. Ways Advantages Disadvantages AMScd supported on Math.SE for a long time no diagonal arrowssyntax less well-knownTwo-way arrows $\rightleftarrows$ look odd array supported on Math.SE for a long timeeasier syntaxwrite basic diagonal arrows like $\nearrow$ fine tuning spacing is harddiagonal arrows only work for neighboring nodes ASCIIFlow WYSIWYG interface lines are rendered as slashes in code TikZ well known syntaxcan draw pretty diagrams not supported on SE, need to import as picture others? [Read More]

## Pandoc LaTeX Mermaid on GitLab CI

Goal To provide an open-source alternative to the Docker image escalope/pandoc-mermaid-plantuml, whose Dockerfile isn’t available. The rationale behind these difficult setup is simple: construct informative Mermaid diagram with intuitive Markdown syntax in an open-source and economic way. This newly constructed Docker image is entirely on GitLab. No Docker Hub account is needed. For sample usage, consult .gitlab-ci.yml in my test project. Difficulties issues raghur/mermaid-filter#51 and #52 issue gitlab-org/gitlab-runner#4566 Useful code/articles time-machine-project/requests-for-comments@470b0c5 Dockerfile Reduce Docker Image Sizes Using Alpine Best practices for building docker images with GitLab CI with the accompanying gist The code block in the highlighted comment in item 2 of the above section pandoc installation for Docker Sample Dockerfile for Alpine Linux in the troubleshooting of Puppeteer sc250024/docker-mermaid-cli@3c9ddb5 src/puppeteerConfigFile. [Read More]

## Mise à jour du template de lettre

### Template de lettre en Xe$\LaTeX$

Contexte J’ai publié mon template de lettre en Xe$\LaTeX$ sur mon ancien blog (hébergé sur GitHub Pages) il y a trois ans. Problème et solution Après le changement de l’ordi portable, il me faut l’installation du pacquetage “texlive-lang-french” sur la nouvelle version d’Ubuntu. Sinon, une erreur du pacquetage Babel se surviendra. ! Package babel Error: Unknown option `frenchb'. Either you misspelled it (babel) or the language definition file frenchb.ldf was not foun d. [Read More]