This is my belated response to a self-identified dupe on TeX.SE.

Background

The list in a \foreach loop is often long.

\foreach \pointA/\pointB in {{(1,0)}/{(2,2)},{(3,4)}/{(2,1)}} {
  \draw \pointA -- \pointB;
}

Imagine having several other loop variables. The code inside the {…} list won’t be readable.

Problem

How can I make it looks smarter?

\foreach \pointA/\pointB in {
  {(1,0)}/{(2,2)},{(3,4)}/{(2,1)}
} {
  \draw \pointA -- \pointB;
}

doesn’t work.

Inspiration

Recently, I was asked the way to make two graphs to illustrate a complex function.

Problem

I had issues in getting a SVG from a TikZ picture containing a pattern filling: https://github.com/mgieseki/dvisvgm/issues/158. The reported issue was created last year, and it’s marked as fixed. Nonetheless, I had this issue even though my MikTeX was up-to-date.

Discussion

1. I wanted to confirm whether my dvisvgm.exe, which had been shipped with MikTeX, was latest.
   • I first asked at https://github.com/mgieseki/dvisvgm/issues/184, but I was referred to MikTeX’s GitHub repository since it’s about the MikTeX-packaged version of this tool.
   • I am not sure about the technical explanation from the owner of dvisvgm at https://github.com/MiKTeX/miktex/issues/1112. It seemed that I was already using the latest stable version of this tool.
2. I gave a MWE illustrating the problem with the graph of y = (x + 1)² with region under the curve filled with a pattern in the above issue. I knew that’s probably off-topic, but the package owner might have some insights about the problem. It turned out that PDF → SVG was partly supported by dvisvgm. Using DVI → SVG, I managed to get the filling pattern, but I lost the beautiful Computer Modern Roman fonts—that’s another issue.
3. Hoping for a response from the owner for the previous problem, I started https://github.com/mgieseki/dvisvgm/issues/186. He suggested the use of --no-fonts or --font-format=woff. I observed no difference in the local filesystem. I uploaded everything I got through GitHub so that he could see what my dvisvgm.exe had output. I didn’t expected that the Computer Modern Roman fonts disappeared on GitHub side. If I hadn’t asked there, I would have never known that it’s the web browser’s security measure not to load the embedded font data in a SVG loaded from a server.

Skills learned

Meaning of some commonly used parameters of dvisvgm:

Background

A secondary school student posted a coordinate geometry question on a Discord homework help server. A helper replied to that question with an illustration of the Perpendicular Distance Formula

where $L$ is the line $Ax + By + C = 0$ without proof.

Goal

To provide an illustrated derivation of this formula.

Recall

A basic property of the dot product: the “algebraic definition” is equivalent to the “geometric definition”.

Goal

Show that

for all $x > 0$.

Proof by inverse functions

Think about their reflection along the line $y = x$ (i.e. their inverse function). Then we get

for all $x \in \Bbb{R}$, which is obviously true.

Proof by definite integrals

Here’s a second proof using definite integrals.

The rectangle $[1,x] \times [0,1]$ contains the region under the graph of the reciprocal $y = 1/x$ in the domain $[1,x]$.

I firsted tried with foreach, but that would create so much paths. I found them difficult to operate on later, for example, with PGF plots library fillbetween. const plot is a better solution.

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{patterns}
\usepgfplotslibrary{fillbetween}
\begin{document}
\newcommand\myN{8}
\pgfplotsset{
    axis lines=center,
    legend style={at={(1,1)},anchor=north east,fill=none},
    title style={at={(0.5,1.05)}},
    every axis x label/.style={
        at={(ticklabel* cs:1)},
        anchor=west,
    },
    every axis y label/.style={
        at={(ticklabel* cs:1)},
        anchor=south,
    },
}
\begin{tikzpicture}
\begin{axis}[
    title={sum of hatched region converges to Euler's constant},
    xlabel={$x$},
    ylabel={$y$},
    xmin=0,
    xmax={\the\numexpr\myN+2},
    ymin=0,
    ymax=1.3,
    xtick=\empty,
    ytick=\empty,
    extra x ticks={1, \myN},
    extra x tick labels={$1$, $n$},
    extra y ticks={1},
]
\addplot[name path=A,domain=1:\myN,samples=501,smooth] {1/x} \closedcycle;
\addlegendentry{$y = \frac{1}{x}$};
\addplot+[domain=1:\myN+1,samples=\myN+1,jump mark left,blue,mark=*,mark options={draw=blue,fill=blue}] {1/x};
\addlegendentry{$y = \frac{1}{\lfloor x \rfloor}$};
\addplot+[name path=B,domain=1:\myN+1,samples=\myN+1,jump mark left,mark=none, draw=none] {1/x} \closedcycle;
\addplot[pattern=north east lines] fill between [of=A and B];
\end{axis}
\end{tikzpicture}
\end{document}

Background

In my previous post about unit circle and trigonometric functions, I included a graph with three trigonometry functions. I’m quite satisfied with my TikZ picture.

Problem

Unluckily, a secondary school student found that my diagram was too complicated.

Solution

\documentclass[tikz,border=2pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{calc}
\newcommand\mytheta{110} %angle theta
\begin{document}
\begin{tikzpicture}[scale=2]
\coordinate[label=left:$O$] (O) at (0,0);
\coordinate[label=above left:${A = (\cos\theta, \sin\theta)}$] (A) at (\mytheta:1);
\coordinate[label=below left:${B = (\cos(-\theta), \sin(-\theta))}$] (B) at (-\mytheta:1);
\coordinate[label=right:$E$] (E) at (1,0);
\draw (O) circle (1);
\draw (A) -- (O)  node [midway, left] {$1$}
    -- (E);
\draw (B) -- (O);
\draw[-stealth] ($(O)!0.3!(E)$) arc (0:\mytheta:0.3) node[midway, above] {$\theta$};
\draw[-stealth] ($(O)!0.25!(E)$) arc (0:{-\mytheta}:0.25) node[midway, below] {$-\theta$};
\end{tikzpicture}
\end{document}

I thought the code would be easy, but it turned out that I spent one hour and half to draw this figure.

\documentclass[border=2pt,preview]{standalone}
\usepackage{tikz}
\usepackage{caption}
\newcommand{\sideA}{2}
\newcommand{\sideB}{3}
\newcommand{\sideC}{6}
\colorlet{myred}{red!40!yellow}
\colorlet{mygreen}{green!40}
\colorlet{myblue}{blue!20}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[thick]
\coordinate (A) at (0,0);
\coordinate (B) at (\sideC,0);
\draw[<->,>=stealth,myred] (A) -- ++ (-\sideA, 0) node [pos=0.5,below] {$\color{myred}{a}$};
\draw[<->,>=stealth,mygreen] (B) -- ++ (\sideB, 0) node [pos=0.5,below] {$\color{mygreen}{b}$};
\draw[<->,>=stealth,myblue] (A) --  (B) node [pos = 0.5, below]{$\color{myblue}{c}$};
\draw[dashed,myred] (A) circle (\sideA);
\draw[dashed,mygreen] (B) circle (\sideB);
\end{tikzpicture}
\captionsetup{labelformat=empty}
\caption{triangle inequality ${\color{myred}{a}} + {\color{mygreen}{b}} >
  {\color{myblue}{c}}$ with $\color{myred}{a = \sideA}$,
  $\color{mygreen}{b = \sideB}$, $\color{myblue}{c = \sideC}$}
\end{figure}
\end{document}

The colors are customized for the Discord bot TeXit.

Problem

In my previous post about LaTeX tables, I used \cellcolor{white} to override the \rowcolor{cyan} in a cell in the leftmost column, which was the column type name.

On Discord, that cell became black because TeXit inverted black and white.

Discussion

I first tried blending black and white, and I found that black!27 and black!28 give a good approximation to Discord’s background color.

Thanks to this Discord Color Palette and a bot command channel on a server, I’ve observed that the desired color is RGB(54,57,62).

This is a first draft of a TikZ picture illustraing this classical formula to be used for math help channels.

Adding \caption{for the picture} without “Figure 1:” requires \usepackage{caption} and wrapping with \begin{figure}. It also possible to use the primitive TeX command \par, but it would be complicated to use that with standalone. In the previous post, the SVG picture from the LaTeX table in an article has too much useless whitespace around the table. I don’t bother to learn other packages, as I need time for other more important stuff.

Inspiration

Number of two-digit numbers not containing the digit ‘8’.

Code

• The standalone class can’t be used with \caption.
• *{8}{c} means 8 c.
• >{\columncolor{cyan}}c gives the column color. It \usepackage[table]{xcolor}.
• \rowcolor{cyan} overrides the column colors.
• \cellcolor{white} overrides the above two commands. It has to be carried out one-by-one without any fancy package.
• \multicolumn{n}{<alignment>}{content} defines a multi-column cell.
• \multirow{n}{*}{content} defines a multi-row cell. It \usepackage{multirow}. It can’t contain \multicolumn.
• \cline{i-j} draws a horizontal line above the row from column i to column j.
• No fancy way of coloring multirow cells without fancy packages.
• \multirow{-9} at the last row creates a cell spanning nine rows from bottom to above, so that its content won’t be covered by colors of former rows.
• \rotatebox[origin=[clr]]{angle}{content}: rotate content by angle anticlockwise with [clr] as the rotation center.

\documentclass[12pt]{article}
\usepackage{multirow}
\usepackage[table]{xcolor}
\usepackage{tikz}
\begin{document}
\begin{table}[htbp]
\centering
\caption{Sample \LaTeX{} multirow table}
\vspace*{1ex}
\label{multiprogram}
\begin{tabular}{|c|c|*{8}{c}>{\columncolor{cyan}}cc|}
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}{}} & \multicolumn{10}{c|}{unit digit} \\\cline{3-12}
\multicolumn{2}{|c|}{} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline
& 1 & &  &  &  &  &  &  &  &  &  \\
& 2 & &  &  &  &  &  &  &  &  &  \\
& 3 & &  &  &  &  &  &  &  &  &  \\
& 4 & &  &  &  &  &  &  &  &  &  \\
& 5 & &  &  &  &  &  &  &  &  &  \\
& 6 & &  &  &  &  &  &  &  &  &  \\
& 7 & &  &  &  &  &  &  &  &  &  \\
\rowcolor{cyan} \cellcolor{white}
& 8 & &  &  &  &  &  &  &  &  &  \\
\multirow{-9}{*}{\rotatebox[origin=c]{90}{tens digit}}
& 9 & &  &  &  &  &  &  &  &  &  \\\hline
\end{tabular}
\end{table}
\end{document}

Result: