# Some math notations from Bulgaria

It is well-known that some of the mathematical notations used internationally differ from those used in the West, for a range of reasons - from economic to linguistic. Yet specific examples usually come as a surprise to an unsuspecting reader. This brief post outlines a few traditions from my own home country, Bulgaria.

Importantly, the examples here are not meant as "universal" notations. Some texts use some of them, others rely more heavily on modern Western notations, and some pick-and-choose based on the subfield of mathematics, or even on expression context.

To illustrate: comma-separated lists will be seen in most texts as in $x,y,z \ldots$ Yet for cases where commas are used in the listed elements (e.g. in scripts), *some* authors will prefer semicolon as in
$$x_{1,2}=\pm \sqrt{z_1}\, ;\, x_{3,4}=\pm \sqrt{z_2}$$

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Math Concept | Notation | Notes
:--- | :--- | :---
multiplication | $a\mathop{.}b$ | using a simple dot for multiply (I believe for 20th century typesetting convenience)
division | $a:b$ | other symbols are also used, but while in Western texts the colon is mostly used for "ratio", in Bulgaria it is also the ordinary "a divided by b".
[decimal comma](https://en.wikipedia.org/wiki/Decimal_separator#Countries_using_decimal_comma) | $3{,}45$ | Spoken as "three whole and fourty-five" ("три цяло и четеридесет и пет") in Bulgarian. As the dot is taken for multiplication, it is not available as a decimal separator.
interval, point | $(1{,}0 ; 1{,}99)$ | semicolon avoids confusion with the decimal comma. Western texts would write $(1.0 , 1.99)$
system of equations (1) | \begin{cases} x+y&=&0\\y&=&1\end{cases}| left brace decorates the group of equations
system of equations (2) | $$ \left\| \begin{array}{lcl} x+y&=&0 \\ y&=&1 \end{array} \right. $$ | left bar decorates the group of equations
arithmetic progression | $$ \div a_1, a_2, \ldots, a_n, \ldots $$ | prefix ÷ annotates the progression
geometric progression | $$ \div\div a_1, a_2, \ldots, a_n, \ldots $$ | prefix ÷÷ annotates the progression
Cyrillic annotations | $L_{шепот} = 20\,\mathrm{dB}$, $L_{крещене} = 70\,\mathrm{dB}$ | contrary to some expectations, the Latin+Greek alphabets are not the only ones in use in math syntax. All Slavic countries employ their scripts for annotations, and in some cases to name variables.
minimum | $$ \underset{x \in [-2;3]}{\mathrm{НМС}}\ f(x) $$ | expanded "Най-Малка Стойност", i.e. "the smallest value". Note the Cyrillic name.
maximum | $$ \underset{x \in [-2;3]}{\mathrm{НГС}}\ f(x) $$ | expanded "Най-Голяма Стойност", i.e. "the biggest value". Note the Cyrillic name.
currency | $x > 100\,\mathrm{лв}$ | "лв" abbreviates "leva", the currency of Bulgaria (BGN). Note the use of Cyrillic.
tangent | $\mathrm{tg}\, 30^\circ$ | contrast "tg" to the Western default "tan"
cotangent | $\mathrm{cotg}\, 30^\circ$ | contrast "cotg" to the Western default "cotan"

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These examples were extracted solely from two elective books I purchased in 2022, targeted at students in the 12th grade. They are:

1. "Математически Справочник", Боряна Дачева Милкоева, ИК "Сънрей" 2019г.
- ISBN: 978-954-8101-09-7

2. "Математика за 12 клас", Кирил Банков, Илиана Цветкова, Даниела Петрова, Гергана Николова, Стефчо Наков. Издателство "Просвета-София" 2021г.
- ISBN: 978-954-01-4121-3

## Aside: Chemistry

A quick check through the national secondary school exit exam ([Matura](https://en.wikipedia.org/wiki/Matura)) also spotted some cyrillic "localization" in chemistry equations:

Chemistry Concept | Notation | Notes
:--- | :--- | :---
gas | $\mathrm{C}\mathrm{O}_{2(г)}$ | note the `(г)` for "газ"
solid | $\mathrm{C}_{(тв)}$ | note the `(тв)` for "твърд"
solution | $$ \mathrm{Cu}\mathrm{O} \stackrel{\mathrm{H}\mathrm{Cl}_{(р-р)}}{\longrightarrow} \mathbf{Б} $$ | note `(р-р)` for "разтвор"/solution, "Б" for variable name
catalyst | $$ \mathbf{А} \stackrel{+H^2 /\mathrm{кат.}}{\longrightarrow} CH_3OH$$ | note the cyrillic "кат." for "каталист"/catalyst, variable name "А"

Last but not least, here is a long equation that keeps all categorical outcomes localized in Bulgarian text (ideally as a single MathML expression):
$$\normalsize \mathrm{Ba} \stackrel{\mathrm{O}_{2}}{\longrightarrow} \text{основен оксид} \stackrel{\mathrm{H}\mathrm{Cl}_{(р-р)}}{\longrightarrow} \text{сол} \stackrel{\mathrm{H}_2\mathrm{S}\mathrm{O}_{4(р-р)}}{\longrightarrow} \text{бяла утайка} $$