## Sekai 🌐 🗺

Sekai is the kanji for 世界, meaning “the world”. That’s a great word because of the scale it designates.

## dvisvgm Guide for TikZ Pictures with Pattern Filling

### A quick note of the right commands for the conversion

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 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. [Read More]

## Distance From a Line

### TikZ figures for a derivation from dot product

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 $$d((x_1,y_1), L) = \frac{\lvert Ax_1 + By_1 + C \rvert}{\sqrt{A^2 + B^2}},$$ 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”. [Read More]

### TikZ figures for some graphical proofs of this inequality

Goal Show that $$\ln (x) \le x - 1$$ 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 $$e^x \ge x + 1$$ for all $x \in \Bbb{R}$, which is obviously true. Proof by definite integrals Here’s a second proof using definite integrals. Case 1: x > 1 The rectangle $[1,x] \times [0,1]$ contains the region under the graph of the reciprocal $y = 1/x$ in the domain $[1,x]$. [Read More]

## A Plot for Euler's Constant

### My first PGF Plot for step functions

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. [Read More]

## LaTeX Table Background Color for 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). [Read More]

## Line Equation in Intercept Form

### LaTeX code for a TikZ figure

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. [Read More]

## LaTeX Multirow Multicol Table Coloring

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. [Read More]