hangulmath¶

Hangul letters as math symbols for LaTeX.

Mathematical notation draws almost entirely on Latin and Greek letters, and a long paper soon runs out of distinct ones. hangulmath adds the 40 letters (jamo) of modern Korean Hangul as math symbols. They are built from simple geometric strokes, look nothing like Latin or Greek, and each one has an established name.

Typeset with hangulmath: a Cauchy–Schwarz-style inequality using the Hangul letter tieut as a sum operator and giyeok as a variable, and the wave equation with mieum as the d'Alembertian

\usepackage{hangulmath}
...
\[ \hangulsum\tiut_{k=1}^{n} \giug_k^{\,2}
   \le \Bigl(\hangulsum\tiut_{k=1}^{n} \giug_k\Bigr)^{2},
   \qquad \mium^2 \vec{A} = -\mu_0 \vec{J} \]

Install Usage and symbol list hangulmath on CTAN

At a glance¶

40 symbols: 14 consonants, 5 double consonants, 10 vowels and 11 compound vowels.
Easy to type: \giyeok follows the official romanization, much as \alpha names α. Every consonant also has a four-letter alias such as \giug, \niun, \diud.
Real math symbols: they take sub- and superscripts, scale in script styles, and work in running text too.
Operators from any symbol: \hangulsum, \hangulint and \hangullim behave like \sum, \int and \lim.
No Korean font needed: the glyphs come from a bundled subset of Noto Sans CJK KR.
Works with kotex in either package order.
Requires XeLaTeX or LuaLaTeX. Released under the LaTeX Project Public License 1.3c; the fonts are under the SIL Open Font License 1.1.

What you can write¶

Every example below was typeset with hangulmath itself.

Consonants as function names¶

ㄱ reads naturally as a function, and ㅁ, which looks like a box, makes a fitting d'Alembertian.

\giug(z) = \frac{1}{\Gamma(z)}, \qquad
\mium = \nabla^2 - \frac{1}{c^2}
        \frac{\partial^2}{\partial t^2}

$Typeset: giyeok of z equals one over Gamma of z, and mieum as the d'Alembertian$

Any symbol as an operator¶

\hangulsum\tiut_{k=1}^{n} k = \frac{n(n+1)}{2}
\hangulint\diud_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}
\hangullim\liul_{n\to\infty}\Bigl(1+\frac1n\Bigr)^{n} = e

$Typeset: tieut as a sum, digeut as an integral, rieul as a limit$

Vowels as brackets¶

ㅓ and ㅏ are mirror images, like ⟨ and ⟩.

\eoh\psi|\phi\ah = \int \psi^*\phi\,dx, \qquad
\sum_n |n\ah\eoh n| = \mathbf{1}

$Typeset: a bra-ket inner product and a completeness relation using the vowels eo and a as angle brackets$

Hamiltonian and Lagrangian¶

i\hbar\,\frac{\partial}{\partial t}|\psi\ah = \piup\,|\psi\ah,
\qquad \piup = p\,\dot q - \liul

$Typeset: the Schrödinger equation with pieup as the Hamiltonian, and pieup equals p q-dot minus rieul$

A new superscript mark¶

A',\ A^*,\ A^\dagger,\ A^{\ciuc}, \qquad
(AB)^{\ciuc} = B^{\ciuc}A^{\ciuc}

$Typeset: chieut used as a superscript mark beside prime, star and dagger$

Arrows¶

ㅗ and ㅛ point up, ㅜ and ㅠ point down.

|\oh\ah,\ |\uh\ah \quad (\text{spin up, down}),
\qquad x \mathrel{\uh} 0

$Typeset: spin up and spin down kets using the vowels o and u as arrows$

Element symbols¶

2\,\kiuk + \piup_2 \to 2\,\kiuk\piup, \qquad
2\,\giug_2 + \iung_2 \rightleftharpoons 2\,\giug_2\iung

$Typeset: chemical equations with Hangul consonants as element symbols$

Get it¶

hangulmath is on CTAN and in TeX Live. The source is on GitHub, and the full manual is hangulmath-doc.pdf. See Install to set it up locally or on Overleaf.