Арабские римские цифры как пишутся

У этого термина существуют и другие значения, см. Цифра (значения).

Эта страница или раздел содержит специальные символы Unicode. Если у вас отсутствуют необходимые шрифты, некоторые символы могут отображаться неправильно.

Ри́мские ци́фры — цифры, использовавшиеся древними римлянами в их непозиционной системе счисления.

Натуральные числа записываются при помощи повторения этих цифр. При этом, если бо́льшая цифра стоит перед меньшей, то они складываются (принцип сложения), если же меньшая стоит перед большей, то меньшая вычитается из большей (принцип вычитания). Последнее правило применяется только во избежание четырёхкратного повторения одной и той же цифры.

Римские цифры появились за 500 лет до нашей эры у этрусков (см. этрусский алфавит), которые могли заимствовать часть цифр у прото-кельтов.

Цифры[править | править код]

Римские обозначения чисел известны ныне лучше, чем любая другая древняя система счисления. Объясняется это не столько какими-то особыми достоинствами римской системы, сколько тем огромным влиянием, которым пользовалась римская империя в сравнительно недавнем прошлом. Этруски, завоевавшие Рим в VII веке до н. э., испытали на себе влияние восточно-средиземноморских культур. Этим отчасти объясняется сходство основных принципов Римской и аттической систем счисления. Обе системы были десятичными, хотя в обеих системах счисления особую роль играло число пять. Обе системы использовали при записи чисел повторяющиеся символы.

Старыми римскими символами для обозначения чисел 1, 5, 10, 100 и 1000 (индо-арабской записи) были, соответственно, символы I, V, X, Θ (или ⊕, или ⊗) и Φ (или ↀ , или CIƆ). Хотя о первоначальном значении этих символов было написано много, их удовлетворительного объяснения нет до сих пор. Согласно одной из распространённых теорий, римская цифра V изображает раскрытую руку с четырьмя прижатыми друг к другу пальцами и отставленным большим пальцем; символ X, согласно той же теории, изображает две скрещённые руки или сдвоенную цифру V. Символы чисел 100 и 1000, возможно, берут начало от греческих букв Θ и φ. Неизвестно, произошли ли более поздние обозначения C и M от старых римских символов или они акрофонически связаны с начальными буквами латинских слов, означавших 100 (центум) и 1000 (милле). Полагают, что римский символ числа 500, буква D, возник из половинки старого символа, обозначавшего 1000. Если не считать, что большинство римских символов скорее всего не были акрофоническими и что промежуточные символы для обозначения чисел 50 и 500 не были комбинациями символов чисел 5 и 10 или 5 и 100, то в остальном римская система счисления напоминала аттическую. Римляне часто использовали принцип вычитания, поэтому иногда вместо VIIII использовали IX ,а XC вместо LXXXX; сравнительно позднее символ IV вместо IIII. Поэтому нынче все римские цифры можно записать заглавными латинскими буквами.

В целом римляне не были склонны заниматься математикой, поэтому не испытывали особой потребности в больших числах. Тем не менее для обозначения 10000 они эпизодически использовали символ CCIƆƆ , а для числа 100000 — символ CCCIƆƆƆ. Половинки этих символов иногда использовались для обозначения чисел 5000 (IƆƆ) и 50000 (IƆƆƆ).

Дроби[править | править код]

Дробей римляне избегали так же упорно, как и больших чисел. В практических задачах, связанных с измерениями, они не использовали дроби, подразделяя единицу измерения обычно на 12 частей, с тем чтобы результат измерения представить в виде составного числа, суммы кратных различных единиц, как это делается сегодня, когда длину выражают в ярдах, футах и дюймах. Английские слова «ounce» (унция) и «inch» (дюйм) происходят от латинского слова лат. uncia (унция), обозначавшего одну двенадцатую основной единицы длины^[1][2].

Символ 1/2 — буква S — использовался в обозначениях номинала монет республиканского периода, однако позднее вышел из употребления. Унция (1/12) обозначалась точкой (·) или (на монетах) в виде маленького выпуклого полушария, иногда – горизонтальной чертой (–), а также (в скорописи) знаками и; обозначением ½ унции (семунции) служили знаки Σ, Є, £, сицилика — Ɔ, секстулы — 𐆓, скрупула — ℈. Однако на практике двенадцатиричные дроби чаще всего изображались сочетанием точек и символа S.

Запись чисел[править | править код]

Для правильной записи больших чисел римскими цифрами необходимо сначала записать число тысяч, затем сотен, затем десятков и, наконец, единиц.

В системе римских цифр отсутствует ноль, но ранее использовалось обозначение нуля как nulla (нет), nihil (ничто) и N (первая буква этих слов).

При этом некоторые из цифр (I, X, C, M) могут повторяться, но не более трёх раз подряд; таким образом, с их помощью можно записать любое натуральное число не более 3999 (MMMCMXCIX). В ранние периоды существовали знаки для обозначения бо́льших цифр — 5000, 10 000, 50 000 и 100 000^{[источник не указан 4466 дней]} (тогда максимальное число по упомянутому правилу равно 399 999). При записи чисел в римской системе счисления меньшая цифра может стоять справа от большей; в этом случае она прибавляется к ней. Например, число 283 по-римски записывается как CCLXXXIII, то есть 100+100+50+30+3=283. Здесь цифра, изображающая сотню, повторена два раза, а цифры, изображающие соответственно десяток и единицу, повторены по три раза.

Пример: число 1988. Одна тысяча M, девять сотен CM, восемь десятков LXXX, восемь единиц VIII. Запишем их вместе: MCMLXXXVIII.

Довольно часто, чтобы выделить числа в тексте, над ними рисовали черту: LXIV. Иногда черту рисовали и сверху, и снизу: XXXII — в частности, так принято выделять римские цифры в русском рукописном тексте (в типографском наборе это не используют из-за технической сложности). У других авторов черта сверху могла обозначать увеличение значения цифры в 1000 раз: V = 5000.

Повсеместно записывать число «четыре» как «IV» стали только в XIX веке, до этого наиболее часто употреблялась запись «IIII». Однако запись «IV» можно встретить уже в документах манускрипта «Forme of Cury», датируемых 1390 годом. На циферблатах часов в большинстве случаев традиционно используется «IIII» вместо «IV», главным образом, по эстетическим соображениям: такое написание обеспечивает визуальную симметрию с цифрами «VIII» на противоположной стороне, а перевёрнутую «IV» прочесть труднее, чем «IIII». Существует и версия, что IV на циферблате не писалось потому, что IV — первые буквы латинского имени бога Юпитера (IVPITER).

Меньшая цифра может быть записана и слева от большей, тогда её следует вычесть из большей. При этом вычитаться могут только цифры, обозначающие 1 или степени 10, а в качестве уменьшаемого выступать только ближайшие в числовом ряду к вычитаемой две цифры (то есть вычитаемое, умноженное на 5 или 10). Повторения меньшей цифры не допускаются. Таким образом, существует только шесть вариантов использования «правила вычитания»:

• IV = 4
• IX = 9
• XL = 40
• XC = 90
• CD = 400
• CM = 900

Например, число 94 будет XCIV = 100 − 10 + 5 − 1 = 94 — так называемое «правило вычитания» (появилось в эпоху поздней античности, а до этого римляне писали число 4 как IIII, а число 40 — как XXXX).

Необходимо отметить, что другие способы «вычитания» недопустимы; так, число 99 должно быть записано как XCIX, но не как IC. Однако, в наши дни в некоторых случаях используется и упрощенная запись римских чисел: например, в программе Microsoft Excel при преобразовании арабских цифр в римские при помощи функции «РИМСКОЕ()» можно использовать несколько видов представления чисел, от классического до сильно упрощённого (так, число 499 может быть записано как CDXCIX, LDVLIV, XDIX, VDIV или ID). Упрощение состоит в том, что для уменьшения какой-либо цифры слева от неё может писаться любая другая цифра:

• 999. Тысяча (M), вычтем 1 (I), получим 999 (IM) вместо CMXCIX. Следствие: 1999 — MIM вместо MCMXCIX
• 95. Сто (C), вычтем 5 (V), получим 95 (VC) вместо XCV
• 1950: Тысяча (M), вычтем 50 (L), получим 950 (LM). Следствие: 1950 — MLM вместо MCML

Случаи такой записи чисел (как правило, годов) часто встречаются в титрах телесериалов США. Например, для года 1998: MIIM вместо MCMXCVIII.

С помощью римских цифр можно записывать и бо́льшие классы чисел. Для этого над теми цифрами, которые обозначают тысячи, ставится черта, а над цифрами, которые обозначают миллионы, — двойная черта. Исключение составляет цифра I; вместо черты сверху записывается цифра M, а начиная с миллиона — по одной черте сверху. Например, число 123123 будет выглядеть так:

CXXIIICXXIII

А миллион как I, но только не с одной, а с двумя чертами во главе: I

Применение[править | править код]

В русском языке римские цифры используют в следующих случаях:

• Номер века или тысячелетия: XIX век, II тысячелетие до н. э.
• Спряжение глаголов.
• Маркировка циферблатов часов «под старину».
• Номер тома в многотомной книге или тома журналов (иногда — номера частей книги, разделов или глав).
• В музыкальной грамоте.
• Порядковый номер монарха, например: Пётр I, Александр III.
• Группа крови на нашивках формы военнослужащих ВС РФ.
• На советских судах обозначали осадку в метрах римскими буквами (на английских кораблях — в футах римскими буквами).
• В некоторых изданиях — номера листов с предисловием к книге, чтобы не исправлять ссылки внутри основного текста при изменении предисловия.
• Иные важные события или пункты списка, например: V постулат Евклида, II мировая война, XX съезд КПСС, Игры XXII Олимпиады и тому подобное.
• Валентность химических элементов, например: оксид серы (IV), хлорид меди (II).
• Номер корпуса в вооружённых силах.
• Год окончания постройки здания на его фронтоне.
• Порядковый номер ступени в звукоряде.
• В математическом анализе римскими цифрами записывают номер производной, правда, при чтении (обычно) произносят «штрих» вместо I, «два штриха» вместо II, «три штриха» вместо III. Наконец, начиная с IV читают «четвёртая производная»: и .

Римские цифры широко употребляли в СССР при указании даты для обозначения месяца года, например: 11/III-85 или 9.XI.89, это можно увидеть на многих архивных документах тех времён. Подобным образом, через косую черту, в том числе записывали дату урока в классных журналах, например, 24/II. Для указания дат жизни и смерти на надгробиях часто использовали особый формат, где месяц года также обозначали римскими цифрами, например, (25 ноября 1887 ~ 26 января 1943). Подобный формат в 1970-1980-х годах использовали в медицинских справках.

С переходом на компьютерную обработку информации форматы даты, основанные на римских цифрах практически вышли из употребления.

В других языках сфера применения римских цифр может иметь особенности. В западных странах римскими цифрами нередко записывают номер года, например, на фронтонах зданий и в титрах видео-, кино- и телепродукции^[3].

В современной Литве на дорожных знаках, на витринах магазинов, на вывесках предприятий римскими цифрами могут обозначать дни недели.

Юникод[править | править код]

Символы со сходным начертанием: L · Լ · լ · ւ · ℒ

Символы со сходным начертанием: D · Д

Символы со сходным начертанием: M · Μ · М · м · Ϻ · ℳ · ᛖ

Символы со сходным начертанием: ʕ · Ҁ · ҁ · Ϟ · Ϛ · Ⴚ

Стандарт Юникода рекомендует использовать для представления римских цифр обычные латинские буквы^[4]. Тем не менее стандарт включает также специальные символы для римских цифр как часть Числовых форм (англ. Number Forms)^[5] в области знаков с кодами с U+2160 по U+2188. Например, MCMLXXXVIII может быть представлено в форме ⅯⅭⅯⅬⅩⅩⅩⅧ. Этот диапазон включает как строчные, так и прописные цифры для записи чисел от 1 (Ⅰ или I) до 12 (Ⅻ или XII), в том числе и комбинированные глифы для составных чисел, таких как 8 (Ⅷ или VIII), главным образом для обеспечения совместимости с восточноазиатскими наборами символов в таких промышленных стандартах, как JIS X 0213, где эти символы определены. Комбинированные глифы используются для представления чисел, которые ранее составлялись из отдельных символов (например, Ⅻ вместо его представления как Ⅹ и Ⅱ). В дополнение к этому, глифы существуют для архаичных^[5] форм записи чисел 1000, 5000, 10 000, большой обратной C (Ɔ), поздней формы записи 6 (ↅ, похожей на греческую стигму: Ϛ), ранней формы записи числа 50 (ↆ, похожей на стрелку, указывающую вниз ↓⫝⊥^[6]), 50 000, и 100 000. Следует отметить, что маленькая обратная c, ↄ не включена в символы римских цифр, но включена в стандарт Юникод как прописная клавдиева буква Ↄ.

Отображение всех этих символов требует наличия программного обеспечения, поддерживающего стандарт Юникод, и шрифта, содержащего соответствующие этим символам глифы (например, шрифт Universalia).

Регулярные выражения[править | править код]

Регулярное выражение для проверки римских цифр — ^(M{0,3})(D?C{0,3}|C[DM])(L?X{0,3}|X[LC])(V?I{0,3}|I[VX])$^[8]
В языке Perl для поиска римских цифр в строке можно использовать регулярное выражение
m/b((?:M{0,3}?(?:D?C{0,3}|C[DM])?(?:L?X{0,3}|X[LC])?(?:I{0,3}?V?I{0,3}|I[VX])))b/gs.

Преобразование[править | править код]

Для преобразования чисел, записанных арабскими цифрами в римские, используются специальные функции.

Например,
в английской версии Microsoft Excel и в любой версии OpenOffice.org Calc для этого существует функция ROMAN (аргумент; форма),
в русской версии Microsoft Excel эта функция называется РИМСКОЕ(число; форма).
Необязательный аргумент «форма» может принимать значения от 0 до 4, а также «Ложь» и «Истина». Отсутствие аргумента «Форма» или равенство его 0 или «Истина» даёт «классическую» (строгую) форму преобразования; значение 4 или «Ложь» даёт наиболее упрощённую; значения 1, 2, 3 дают промежуточные по строгости-упрощению варианты. Различия проявляются, например, на числах 45, 49, 495, 499 (указаны первые в диапазоне [1;3999]).

Для нецелых значений аргумента «число» производится округление вниз до целого; если после этого значение оказывается больше 3999 или меньше 0, то функция возвращает «#Знач»; для значения 0 возвращается пустая ячейка.

var arab = [1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000];
var roman = ['I','IV','V','IX','X','XL','L','XC','C','CD','D','CM','M'];

function arabToRoman(number)
{
	if(!number) return '';

	var ret = '';
	var i = arab.length - 1;
	while(number > 0)
	{
		if(number >= arab[i])
		{
			ret += roman[i];
			number -= arab[i];
		}
		else
		{
			i--;
		}
	
	}
	return ret;
}

function romanToArab(str)
{
	
	str = str.toUpperCase();

	var ret = 0;
	var i = arab.length - 1;
	var pos = 0;
	while(i >= 0 && pos < str.length )
	{
		if(str.substr(pos, roman[i].length) == roman[i])
		{
			ret += arab[i];
			pos += roman[i].length;
		}
		else
		{
			i--;
		}
	
	}
	return ret;
}

#include <string.h> const int arabar[] = { 1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000}; const char *romanar[] = { "I", "IV", "V", "IX", "X", "XL", "L", "XC", "C", "CD", "D", "CM", "M"};   char *arab2roman(unsigned short int arab) {  static char roman[80];  const int m = sizeof(arabar)/sizeof(int)-1, arabmax=arabar[m];  const char romanmax=romanar[m][0];  int i, n;  if(!arab) {  *roman=0;  return roman;  }  i=0;  while(arab>arabmax) {  roman[i++] = romanmax;  arab -= arabmax;  }  n=m;  while(arab > 0) {  if(arab >= arabar[n]) {  roman[i++] = romanar[n][0];  if(n&1)  roman[i++] = romanar[n][1];  arab -= arabar[n];  } else  n--;  }  roman[i]=0;  return roman; } unsigned short int roman2arab(char *roman) {  const int m = sizeof(arabar)/sizeof(int)-1;  unsigned short int arab;  int len, n, i, pir;  len=strlen(roman);  arab=0;  n=m;  i=0;  while(n >= 0 && i < len) {  pir=n&1;  if(roman[i] == romanar[n][0] && (!pir || roman[i+1] == romanar[n][1])) {  arab += arabar[n];  i += 1+pir;  } else  n--;  }  return arab; } 

val arabar = Array(1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000) val romanar = Array("I", "IV", "V", "IX", "X", "XL", "L", "XC", "C", "CD", "D", "CM", "M") def arab2roman(arab: Int, acc: String = "", n: Int = arabar.length - 1): String = if (arab == 0) acc else if (arab >= arabar(n)) arab2roman(arab - arabar(n), acc + romanar(n), n) else arab2roman(arab, acc, n-1) // arab2roman(4933) = MMMMCMXXXIII 

type str2 = string[2]; const Rims : array[1..14] of str2 = ('M','CM','D','CD','C','XC','L','XL','X','IX','V','IV','I',' '); Arab : array[1..14] of integer = (1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1, 0); var N, NI, I, J : integer; S : string; function Arab2Rim(N : integer) : string; var S : string; I : integer; begin S := ''; I:=1; while N > 0 do begin while Arab[I]<=N do begin S := S + Rims[I]; N := N - Arab[I] end; I:=I+1 end; Arab2Rim := S end; function Rim2Arab (S:string) : integer; var I, N : integer; begin I:=1; N := 0; while S<>'' do begin while Rims[I] = Copy(S, 1, Length(Rims[I]) ) do begin S := Copy( S, 1+Length(Rims[I]), 255); N := N + Arab[I] end; I:=I+1 end; Rim2Arab := N end; begin WriteLn('Перевод из арабских цифр в римские. 1999 B_SA'); { Write('Введите число для преобразования:'); ReadLn(N);} for NI := 26 to 46 do WriteLn(NI,' = ',Arab2Rim(NI),' обратно ', Rim2Arab( Arab2Rim(NI) )); end. 

function Arab2Roman(arab:integer):string; var  i:integer;  d:integer;  arab_str:string;  arab_len:integer; begin  Result := '';  arab_str := IntToStr(arab);  arab_len := Length(arab_str);  for i := 0 to arab_len-1 do begin  d := StrToInt(String(arab_str[arab_len-i]));  if (d+1) mod 5 = 0 then  Result := Copy('IXCM', 1+i, 1) + Copy('VXLCDM', i*2 + (d+1) div 5, 1) + Result  else  Result := Copy('VLD', 1+i, d div 5) + Copy('IIIXXXCCCMMM', 1+i*3, (d mod 5)) + Result;  end; end; 

10 INPUT "АРАБСКОЕ ЧИСЛО: "; А$ 20 FOR I=0 TO LEN(A$)-1 30 X=VAL(MID$(A$,LEN(A$)-I,1)) 40 IF X=4 OR X=9 THEN B$=MID$("IXCM",I+1,1)+MID$("VXLCDM",I*2+(X+1)/5,1)+B$ 50 IF X<4 THEN B$=MID$("IIIXXXCCCMMM",1+I*3,X)+B$  ELSE IF X>4 AND X<9 THEN B$=MID$("VLD",I+1,1)+MID$("IIIXXXCCCMMM",1+I*3,X-5)+B$ 60 NEXT I 70 PRINT "РИМСКОЕ ЧИСЛО: "; B$ 

string-join(  for $num in (1999)  return (  ('','M','MM','MMM')[($num idiv 1000) mod 10+1],  ('','C','CC','CCC','CD','D','DC','DCC','DCCC','CM')[($num idiv 100) mod 10+1],  ('','X','XX','XXX','XL','L','LX','LXX','LXXX','XC')[($num idiv 10) mod 10+1],  ('','I','II','III','IV','V','VI','VII','VIII','IX')[$num mod 10+1]  ),  '') 

use strict; use warnings; my $n = 1999; my $nums = [   ['', qw(I II III IV V VI VII VIII IX) ],  ['', qw(X XX XXX XL L LX LXX LXXX XC) ],  ['', qw(C CC CCC CD D DC DCC DCCC CM) ],  ['', qw(M MM MMM) ] ]; my $i = 0; my @res = (); push @res, ($nums->[$i++][ ($n % 10, $n = int($n / 10))[0] ]) for 0 .. 3; print reverse @res; 

import java.util.*; public class IntegerConverter { public static String intToRoman(int number) { if (number >= 4000 || number <= 0) return null; StringBuilder result = new StringBuilder(); for(Integer key : units.descendingKeySet()) { while (number >= key) { number -= key; result.append(units.get(key)); } } return result.toString(); } private static final NavigableMap<Integer, String> units; static { NavigableMap<Integer, String> initMap = new TreeMap<>(); initMap.put(1000, "M"); initMap.put(900, "CM"); initMap.put(500, "D"); initMap.put(400, "CD"); initMap.put(100, "C"); initMap.put(90, "XC"); initMap.put(50, "L"); initMap.put(40, "XL"); initMap.put(10, "X"); initMap.put(9, "IX"); initMap.put(5, "V"); initMap.put(4, "IV"); initMap.put(1, "I"); units = Collections.unmodifiableNavigableMap(initMap); } } 

/// <summary> /// Класс предназначен для преобразований арабских чисел в римские и обратно /// </summary> /// <remarks> /// <para>Класс изначально содержит алфавит римских чисел, способных определять арабские числа от 1 до 39999</para> /// <para>Если необходимо расширить диапазон, то можно определить дополнительные обозначения для римских чисел, используя /// поле <see cref="БазовыеРимскиеЧисла"/>БазовыеРимскиеЧисла</remarks> public static class РимскоеЧисло { /// <summary> /// Алфавит базовых римских чисел /// <para>Алфавит построен в виде словаря. Ключом словаря является арабское число (int), значением - соответствующее ему /// римское число (string)</para> /// </summary> /// <remarks> /// <para>Содержит римское обозначения арабских чисел 1*,4*,5*,9* - где "*"представляет собой 0...N нулей</para> /// <para>При создании содержит в себе обозначение чисел от 1 до 10000 (I...ↂ) Так как в римском числе один символ не может /// встречаться более трех раз, то изначально можно преобразовать в римский формат числа от 1 до 39999.</para>  /// <para>Если Вы хотите иметь возможность работать с большим количеством римских чисел, то вы должны добавить в список  /// дополнительные обозначения начиная с 40000 не пропуская элементы 1*,4*,5*,9*.</para> /// </remarks> public static SortedList<int, string> БазовыеРимскиеЧисла { get; set; } static РимскоеЧисло() {  БазовыеРимскиеЧисла = new SortedList<int, string>(17);  БазовыеРимскиеЧисла.Add(1, "I");  БазовыеРимскиеЧисла.Add(4, "IV");  БазовыеРимскиеЧисла.Add(5, "V");  БазовыеРимскиеЧисла.Add(9, "IX");  БазовыеРимскиеЧисла.Add(10, "X");  БазовыеРимскиеЧисла.Add(40, "XL");  БазовыеРимскиеЧисла.Add(50, "L");  БазовыеРимскиеЧисла.Add(90, "XC");  БазовыеРимскиеЧисла.Add(100, "C");  БазовыеРимскиеЧисла.Add(400, "CD");  БазовыеРимскиеЧисла.Add(500, "D");  БазовыеРимскиеЧисла.Add(900, "CM");  БазовыеРимскиеЧисла.Add(1000, "M");  БазовыеРимскиеЧисла.Add(4000, "Mↁ");  БазовыеРимскиеЧисла.Add(5000, "ↁ");  БазовыеРимскиеЧисла.Add(9000, "Mↂ");  БазовыеРимскиеЧисла.Add(10000, "ↂ"); } /// <summary> /// Рассчитывает максимально возможное римское число для текущего алфавита римских чисел. /// </summary> /// <returns>Максимально возможное римское число</returns> public static uint МаксимальноеРимскоеЧисло()  {   int последнееЧисло = БазовыеРимскиеЧисла.Keys.Last();  int числоБезНулей = int.Parse(последнееЧисло.ToString().Replace('0',''));  int предварительное=0;    switch (числоБезНулей)  {  case 1:  предварительное = последнееЧисло * 4 - 1;  break;  case 4:  case 9:  предварительное = последнееЧисло;  break;  case 5:  предварительное = последнееЧисло + последнееЧисло / 5 * 3;  break;  default:  break;  }  return uint.Parse(предварительное.ToString().Replace('0', '9'));;  } /// <summary> /// Конвентирует целое число в римское число /// </summary> /// <param name="числоАраб">Арабское число, которое необходимо преобразовать в римскую запись</param> /// <exception cref="ArgumentOutOfRangeException">Генерируется когда в качестве параметра передано число равное "0"  /// или число большее чем максимальная римское число.</exception> /// <returns>Строку, представляющую собой римской число</returns> public static string АрабскоеВРимское(this int числоАраб) {  StringBuilder числоРимское = new StringBuilder();  //Исключаем знак "-" из арабского числа и делаем его первым символом римского числа  if (числоАраб < 0)  {  числоРимское.Append("-");  числоАраб = -числоАраб;  }  if (числоАраб == 0)  throw new ArgumentOutOfRangeException("числоАраб", числоАраб,   "Недопустимое значение аргумента: римские числа не могут быть равными"0"");  else if (числоАраб > МаксимальноеРимскоеЧисло())  throw new ArgumentOutOfRangeException("числоАраб", числоАраб,   string.Format("Недопустимое значение аргумента: невозможно задать римское число большее чем {0}",  МаксимальноеРимскоеЧисло()));  //Раскладываем арабское число на составляющие его римские числа и объединяем их в одну строку  var необходимыеБазовыеРимскиеЧисла =   from к in БазовыеРимскиеЧисла.Keys   where к <= числоАраб   orderby к descending   select к;  foreach (int тек in необходимыеБазовыеРимскиеЧисла)  {  while ((числоАраб / тек) >= 1)  {  числоАраб -= тек;  числоРимское.Append(БазовыеРимскиеЧисла[тек]);  }  }  return числоРимское.ToString(); } /// <summary> /// Конвентирует римское число в арабское /// </summary> /// <param name="числоРимское">Римское число, которое необходимо преобразовать в тип int</param> /// <exception cref="FormatException">Генерируется когда в качестве параметра передано число не являющееся римским</exception> /// <returns>Целое число, представляющее собой арабскую запись римского числа</returns> public static int РимскоеВАрабское(this string числоРимское) {  int числоАраб = 0;  sbyte отрицательное = 1;  string рим = числоРимское.Trim();  if (рим[0] == '-')  {  отрицательное = -1;  рим = рим.Substring(1);  }  StringBuilder шаблонРимскогоНомера = new StringBuilder();    foreach (int к in БазовыеРимскиеЧисла.Keys)  {  int индекс = БазовыеРимскиеЧисла.Keys.IndexOf(к);  string квантификатор="?";  if (индекс == 0 || (индекс % 4) == 0)  квантификатор="{0,3}";  шаблонРимскогоНомера.Insert(0, string.Format("(?<{0}>({1}){2})?", к.ToString(),   БазовыеРимскиеЧисла[к], квантификатор));  }  //Игнорировать регистр + соответствие должно начинаться с начала строки  шаблонРимскогоНомера.Insert(0, "(?i)^");  //Соответствие должно обнаруживаться в конце строки  шаблонРимскогоНомера.Append("$");  //Упрощенная проверка. Не проверяет таких ошибок как IVII  if (!Regex.IsMatch(рим, шаблонРимскогоНомера.ToString()))  throw new FormatException(string.Format("Текст "{0}" не является римским числом",числоРимское));  Match число = Regex.Match(рим, шаблонРимскогоНомера.ToString());    foreach (int к in БазовыеРимскиеЧисла.Keys)  {  числоАраб += число.Groups[к.ToString()].Length / БазовыеРимскиеЧисла[к].Length * к;  }    return числоАраб * отрицательное; } } 

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• Арабские цифры
• Символы древнеримских денежных и весовых единиц

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven:

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notations IV and IX can be read as «one less than five» (4) and «one less than ten» (9), although there is a tradition favouring representation of «4» as «IIII» on Roman numeral clocks.^[1]

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying «a thousand, and a hundred less than another thousand», means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000. The current year is MMXXIII (2023).

Description

Roman numerals use different symbols for each power of ten and no zero symbol, in contrast with the place value notation of Arabic numerals (in which place-keeping zeros enable the same digit to represent different powers of ten).

This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and became thoroughly chaotic in medieval times. Even the post-renaissance restoration of a largely «classical» notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved «flexibility».^[2] On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law (where an «incorrect» or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period)^[3] it is desirable to strictly follow the usual style described below.

Standard form

The following table displays how Roman numerals are usually written:^[4]

Individual decimal places

The numerals for 4 (IV) and 9 (IX) are written using «subtractive notation»,^[5] where the first symbol (I) is subtracted from the larger one (V, or X), thus avoiding the clumsier IIII and VIIII.^[a] Subtractive notation is also used for 40 (XL), 90 (XC), 400 (CD) and 900 (CM).^[6] These are the only subtractive forms in standard use.

A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

•    39 = XXX + IX = XXXIX.
•   246 = CC + XL + VI = CCXLVI.
•   789 = DCC + LXXX + IX = DCCLXXXIX.
• 2,421 = MM + CD + XX + I = MMCDXXI.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:

•   160 = C + LX = CLX
•   207 = CC + VII = CCVII
• 1,009 = M + IX = MIX
• 1,066 = M + LX + VI = MLXVI^[7][8]

In practice, Roman numerals for numbers over 1000 ^[b] are currently used mainly for year numbers, as in these examples:

• 1776 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty).
• 1918 = M + CM + X + VIII = MCMXVIII (the first year of the Spanish flu pandemic)
• 1954 = M + CM + L + IV = MCMLIV (as in the trailer for the movie The Last Time I Saw Paris)^[3]
• 2014 = MM + X + IV = MMXIV (the year of the games of the XXII (22nd) Olympic Winter Games (in Sochi, Russia))

The largest number that can be represented in this notation is 3,999 (MMMCMXCIX), but since the largest Roman numeral likely to be required today is MMXXIII (the current year) there is no practical need for larger Roman numerals. Prior to the introduction of Arabic numerals in the West, ancient and medieval users of the system used various means to write larger numbers; see large numbers below.

Other forms

Forms exist that vary in one way or another from the general standard represented above.

Other additive forms

While subtractive notation for 4, 40 and 400 (IV, XL and CD) has been the usual form since Roman times, additive notation to represent these numbers (IIII, XXXX and CCCC)^[9] continued to be used, including in compound numbers like XXIIII,^[10] LXXIIII,^[11] and CCCCLXXXX.^[12] The additive forms for 9, 90, and 900 (VIIII,^[9] LXXXX,^[13] and DCCCC^[14]) have also been used, although less often.

The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to the Colosseum, IIII is systematically used instead of IV, but subtractive notation is used for XL; consequently, gate 44 is labelled XLIIII.^[15][16]

Modern clock faces that use Roman numerals still very often use IIII for four o’clock but IX for nine o’clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.^[17][18][19] However, this is far from universal: for example, the clock on the Palace of Westminster tower (commonly known as Big Ben) uses a subtractive IV for 4 o’clock.^[18]

Isaac Asimov once mentioned an «interesting theory» that Romans avoided using IV because it was the initial letters of IVPITER, the Latin spelling of Jupiter, and might have seemed impious.^[20] He did not say whose theory it was.

Several monumental inscriptions created in the early 20th century use variant forms for «1900» (usually written MCM). These vary from MDCCCCX for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for 1903, on the north entrance to the Saint Louis Art Museum.^[21]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written IIIII and XXXXX instead of V and L, and there are instances such as IIIIII and XXXXXX rather than VI or LX.^[22][23]

Other subtractive forms

There is a common belief that any smaller digit placed to the left of a larger digit is subtracted from the total, and that by clever choices a long Roman numeral can be «compressed». The best known example of this is the ROMAN() function in Microsoft Excel, which can turn 499 into CDXCIX, LDVLIV, XDIX, VDIV, or ID depending on the «Form» setting.^[24] There is no indication this is anything other than an invention by the programmer, and the universal-subtraction belief may be a result of modern users trying to rationalize the syntax of Roman numerals.

There is, however, some historic use of subtractive notation other than that described in the above «standard»: in particular IIIXX for 17,^[25] IIXX for 18,^[26] IIIC for 97,^[27] IIC for 98,^[28][29] and IC for 99.^[30] A possible explanation is that the word for 18 in Latin is duodeviginti, literally «two from twenty», 98 is duodecentum (two from hundred), and 99 is undecentum (one from hundred).^[31] However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.

There are multiple examples of IIX being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than VIII. XIIX was used by officers of the XVIII Roman Legion to write their number.^[32][33] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.^[34]

Rare variants

While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.

• IIXX was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say «twenty-second» in Latin, namely duo et vice(n)sima (literally «two and twentieth») rather than the «regular» vice(n)sima secunda (twenty second).^[35] Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of «22nd Legion» stood for 18, and «corrected» it to XVIII.^[35]

• There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as XVIXIII, corresponding to the common reading «sixteen thirteen» of such year numbers in English, or 1519 as XV^CXIX as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.^[37]
• In some French texts from the 15th century and later one finds constructions like IIII^XXXIX for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen).^[37] Similarly, in some English documents one finds, for example, 77 written as «iii^xxxvii» (which could be read «three-score and seventeen»).^[38]
• A medieval accounting text from 1301 renders numbers like 13,573 as «XIII. M. V. C. III. XX. XIII«, that is, «13×1000 + 5×100 + 3×20 + 13».^[39]
• Other numerals that do not fit the usual patterns – such as VXL for 45, instead of the usual XLV — may be due to scribal errors, or the writer’s lack of familiarity with the system, rather than being genuine variant usage.

Non-numeric combinations

As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, «XXX» and «XL» have other connotations in addition to their values as Roman numerals, while «IXL» more often than not is a gramogram of «I excel», and is in any case not an unambiguous Roman numeral.^[40]

Zero

As a non-positional numeral system, Roman numerals have no «place-keeping» zeros. Furthermore, the system as used by the Romans lacked a numeral for the number zero itself (that is, what remains after 1 is subtracted from 1). The word nulla (the Latin word meaning «none») was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from 525 AD.^[41][42] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for «nothing») for 0, in a table of epacts, all written in Roman numerals.^[43]

The use of N to indicate «none» long survived in the historic apothecaries’ system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.^[44]

Fractions

The base «Roman fraction» is S, indicating 1⁄2.
The use of S (as in VIIS to indicate 71⁄2) is attested in some ancient inscriptions^[45]
and also in the now rare apothecaries’ system (usually in the form SS):^[44] but while Roman numerals for whole numbers are essentially decimal S does not correspond to 5⁄10, as one might expect, but 6⁄12.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 2² × 3) makes it easier to handle the common fractions of 1⁄3 and 1⁄4 than does a system based on ten (10 = 2 × 5). Notation for fractions other than 1⁄2 is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit as. Fractions less than 1⁄2 are indicated by a dot (·) for each uncia «twelfth», the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is S for semis «half». Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine.^[46] The arrangement of the dots was variable and not necessarily linear. Five dots arranged like (⁙) (as on the face of a die) are known as a quincunx, from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.

Each fraction from 1⁄12 to 12⁄12 had a name in Roman times; these corresponded to the names of the related coins:

Other Roman fractional notations included the following:

Large numbers

During the centuries that Roman numerals remained the standard way of writing numbers throughout Europe, there were various extensions to the system designed to indicate larger numbers, none of which were ever standardised.

Apostrophus

One of these was the apostrophus,^[47] in which 500 was written as IↃ, while 1,000 was written as CIↃ.^[20] This is a system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses), which has its origins in Etruscan numeral usage.

Each additional set of C and Ↄ surrounding CIↃ raises the value by a factor of ten: CCIↃↃ represents 10,000 and CCCIↃↃↃ represents 100,000. Similarly, each additional Ↄ to the right of IↃ raises the value by a factor of ten: IↃↃ represents 5,000 and IↃↃↃ represents 50,000. Numerals larger than CCCIↃↃↃ do not occur.^[48]

Sometimes CIↃ was reduced to ↀ for 1,000. Similarly, IↃↃ for 5,000 was reduced to ↁ; CCIↃↃ for 10,000 to ↂ; IↃↃↃ for 50,000 to ↇ (ↇ); and CCCIↃↃↃ (ↈ) for 100,000 to ↈ.
^[49]

IↃ and CIↃ most likely preceded, and subsequently influenced, the adoption of «D» and «M» in Roman numerals.

John Wallis is often credited for introducing the symbol for infinity ⟨∞⟩, and one conjecture is that he based it on ↀ, since 1,000 was hyperbolically used to represent very large numbers.

Vinculum

Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a «bar» or «overline».^[49] It was a common alternative to the apostrophic ↀ during the Imperial era: both systems were in simultaneous use around the Roman world (M for ‘1000’ was not in use until the Medieval period).^[50]
[51]
The use of vinculum for multiples of 1,000 can be observed, for example, on the milestones erected by Roman soldiers along the Antonine Wall in the mid-2nd century AD.^[52] The vinculum for marking 1,000s continued in use in the Middle Ages, though it became known more commonly as titulus.^[53]

Some modern sources describe the vinculum as if it were a part of the current «standard».^[54] However, this is purely hypothetical, since no common modern usage requires numbers larger than the current year (MMXXIII). Nonetheless, here are some examples, to give an idea of how it might be used:

• IV = 4,000
• IVDCXXVII = 4,627
• XXV = 25,000
• XXVCDLIX = 25,459

This use of lines is distinct from the custom, once very common, of adding both underline and overline (or very large serifs) to a Roman numeral, simply to make it clear that it is a number, e.g.
for 1967. There is some scope for confusion when an overline is meant to denote multiples of 1,000, and when not. The Greeks and Romans often overlined letters acting as numerals to highlight them from the general body of the text, without any numerical significance. This stylistic convention was, for example, also in use in the inscriptions of the Antonine Wall,^[55] and the reader is required to decipher the intended meaning of the overline from the context.

Another medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10:^{[citation needed]} thus M for 10,000 as an alternative form for X. In combination with the overline the bracketed forms might be used to raise the multiplier to ten thousand, thus:

• VIII for 80,000
• XX for 200,000

This same syntax may also have indicated multiplication by 100^{[citation needed]} so the above two examples are 800,000 and 2,000,000.

Origin

The system is closely associated with the ancient city-state of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.

Etruscan numerals

Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

The Roman numerals, in particular, are directly derived from the Etruscan number symbols: ⟨𐌠⟩, ⟨𐌡⟩, ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ for 1, 5, 10, 50, and 100 (They had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since Etruscan was written from right to left.)^[56]

The symbols ⟨𐌠⟩ and ⟨𐌡⟩ resembled letters of the Etruscan alphabet, but ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as 𐌠𐌠𐌠𐌢𐌢, 𐌠𐌠𐌢𐌢, and 𐌠𐌢𐌢, mirroring the way they spoke those numbers («three from twenty», etc.); and similarly for 27, 28, 29, 37, 38, etc. However, they did not write 𐌠𐌡 for 4 (nor 𐌢𐌣 for 40), and wrote 𐌡𐌠𐌠, 𐌡𐌠𐌠𐌠 and 𐌡𐌠𐌠𐌠𐌠 for 7, 8, and 9, respectively.^[56]

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: ⟨𐌠⟩, ⟨𐌢⟩, and ⟨𐌟⟩. The symbols for 5 and 50 changed from ⟨𐌡⟩ and ⟨𐌣⟩ to ⟨V⟩ and ⟨ↆ⟩ at some point. The latter had flattened to ⟨⊥⟩ (an inverted T) by the time of Augustus, and soon afterwards became identified with the graphically similar letter ⟨L⟩.^[48]

The symbol for 100 was written variously as ⟨𐌟⟩ or ⟨ↃIC⟩, and was then abbreviated to ⟨Ↄ⟩ or ⟨C⟩, with ⟨C⟩ (which matched the Latin letter C) finally winning out. It might have helped that C was the initial letter of CENTUM, Latin for «hundred».

The numbers 500 and 1000 were denoted by V or X overlaid with a box or circle. Thus 500 was like a Ↄ superimposed on a Þ. It became D or Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified as the letter D; an alternative symbol for «thousand» was a CIↃ, and half of a thousand or «five hundred» is the right half of the symbol, IↃ, and this may have been converted into D.^[20]

The notation for 1000 was a circled or boxed X: Ⓧ, ⊗, ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. Over time, the symbol changed to Ψ and ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille «thousand».^[48]

According to Paul Kayser, the basic numerical symbols were I, X, C and Φ (or ⊕) and the intermediate ones were derived by taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).^[57]

Classical Roman numerals

The Colosseum was constructed in Rome in CE 72–80,^[58] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,^[59] to demonstrate that in Imperial times Roman numerals had already assumed their classical form: as largely standardised in current use. The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation — while XL is used for 40, IV is avoided in favour of IIII: in fact gate 44 is labelled XLIIII.

Use in the Middle Ages and Renaissance

Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: i, ii, iii, iv, and so on.

Since the Middle Ages, a «j» has sometimes been substituted for the final «i» of a «lower-case» Roman numeral, such as «iij» for 3 or «vij» for 7. This «j» can be considered a swash variant of «i«. Into the early 20th century, the use of a final «j» was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.^[60]

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called «medieval Roman numerals». Some simply substitute another letter for the standard one (such as «A» for «V«, or «Q» for «D«), while others serve as abbreviations for compound numerals («O» for «XI«, or «F» for «XL«). Although they are still listed today in some dictionaries, they are long out of use.^[61]

Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient «Arabic» equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

• Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers and are usually read as ordinals; e.g. II is pronounced «the second». This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
• Generational suffixes, particularly in the U.S., for people sharing the same name across generations, for example William Howard Taft IV. These are also usually read as ordinals.
• In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
• The year of production of films, television shows and other works of art within the work itself. Outside reference to the work will use regular Arabic numerals.

• Hour marks on timepieces. In this context, 4 is often written IIII.
• The year of construction on building façades and cornerstones.
• Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
• Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
• Sequels to some films, video games, and other works (as in Rocky II, Grand Theft Auto V).
• Outlines that use numbers to show hierarchical relationships.
• Occurrences of a recurring grand event, for instance:
  • The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad).
  • The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XLII; Super Bowl 50 was a one-time exception^[64]).
  • WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.

Specific disciplines

In astronautics, United States rocket model variants are sometimes designated by Roman numerals, e.g. Titan I, Titan II, Titan III, Saturn I, Saturn V.

In astronomy, the natural satellites or «moons» of the planets are traditionally designated by capital Roman numerals appended to the planet’s name. For example, Titan’s designation is Saturn VI.

In chemistry, Roman numerals are often used to denote the groups of the periodic table. They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.

In education, school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, «grade IX» is sometimes seen for «grade 9».

In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

In graphic design stylised Roman numerals may represent numeric values.

In law, Roman numerals are commonly used to help organize legal codes as part of an alphanumeric outline.

In advanced mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2-era German III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

• Movements are often numbered using Roman numerals.
• In Roman Numeral Analysis, harmonic function is identified using Roman Numerals.
• Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries’ system of measurement: including SS to denote «one half» and N to denote «zero».^[44][65]

In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.

In seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale of earthquakes.

In sport the team containing the «top» players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the «1st XV«, while a lower-ranking cricket or American football team might be the «3rd XI«.

In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.

In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for «seventy»).

Modern use in European languages other than English

Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe and in other regions (e.g. Latin America) that use a European language other than English. For instance:

Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French XVIII^e siècle^[66] and the Spanish siglo XVIII mean «18th century». Slavic languages in and adjacent to Russia similarly favor Roman numerals (xviii век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes «18.» (with a period) before the local word for «century».

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals, while the day is in Arabic numerals: «4.VI.1789″ and «VI.4.1789″ both refer unambiguously to 4 June 1789.

Roman numerals are sometimes used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,^[67] and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is closed on Sundays. Note that the listing uses 24-hour time.

Roman numerals may also be used for floor numbering.^[68][69] For instance, apartments in central Amsterdam are indicated as 138-III, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as 138-huis.

In Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX/17 thus marks 17.9 km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the Italian Parliament from 2018 to 2022 (elected in the 2018 Italian general election) is called the XVIII Legislature of the Italian Republic (or more commonly the «XVIII Legislature»).

A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The «Number Forms» block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.^[70] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that «[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters».^[71]
The block also includes some apostrophus symbols for large numbers, an old variant of «L» (50) similar to the Etruscan character, the Claudian letter «reversed C», etc.

See also

References

Notes

Citations

Sources

• Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8.

Further reading

• Aczel, Amir D. 2015. Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers. 1st edition. New York: Palgrave Macmillan.
• Goines, David Lance. A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals. Boston: D.R. Godine, 1982.
• Houston, Stephen D. 2012. The Shape of Script: How and Why Writing Systems Change. Santa Fe, NM: School for Advanced Research Press.
• Taisbak, Christian M. 1965. «Roman numerals and the abacus.» Classica et medievalia 26: 147–60.

External links

• «Roman Numerals (Totally Epic Guide)». Know The Romans.

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven:

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notations IV and IX can be read as «one less than five» (4) and «one less than ten» (9), although there is a tradition favouring representation of «4» as «IIII» on Roman numeral clocks.^[1]

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying «a thousand, and a hundred less than another thousand», means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000. The current year is MMXXIII (2023).

Description

Roman numerals use different symbols for each power of ten and no zero symbol, in contrast with the place value notation of Arabic numerals (in which place-keeping zeros enable the same digit to represent different powers of ten).

This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and became thoroughly chaotic in medieval times. Even the post-renaissance restoration of a largely «classical» notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved «flexibility».^[2] On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law (where an «incorrect» or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period)^[3] it is desirable to strictly follow the usual style described below.

Standard form

The following table displays how Roman numerals are usually written:^[4]

Individual decimal places

The numerals for 4 (IV) and 9 (IX) are written using «subtractive notation»,^[5] where the first symbol (I) is subtracted from the larger one (V, or X), thus avoiding the clumsier IIII and VIIII.^[a] Subtractive notation is also used for 40 (XL), 90 (XC), 400 (CD) and 900 (CM).^[6] These are the only subtractive forms in standard use.

A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

•    39 = XXX + IX = XXXIX.
•   246 = CC + XL + VI = CCXLVI.
•   789 = DCC + LXXX + IX = DCCLXXXIX.
• 2,421 = MM + CD + XX + I = MMCDXXI.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:

•   160 = C + LX = CLX
•   207 = CC + VII = CCVII
• 1,009 = M + IX = MIX
• 1,066 = M + LX + VI = MLXVI^[7][8]

In practice, Roman numerals for numbers over 1000 ^[b] are currently used mainly for year numbers, as in these examples:

• 1776 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty).
• 1918 = M + CM + X + VIII = MCMXVIII (the first year of the Spanish flu pandemic)
• 1954 = M + CM + L + IV = MCMLIV (as in the trailer for the movie The Last Time I Saw Paris)^[3]
• 2014 = MM + X + IV = MMXIV (the year of the games of the XXII (22nd) Olympic Winter Games (in Sochi, Russia))

The largest number that can be represented in this notation is 3,999 (MMMCMXCIX), but since the largest Roman numeral likely to be required today is MMXXIII (the current year) there is no practical need for larger Roman numerals. Prior to the introduction of Arabic numerals in the West, ancient and medieval users of the system used various means to write larger numbers; see large numbers below.

Other forms

Forms exist that vary in one way or another from the general standard represented above.

Other additive forms

While subtractive notation for 4, 40 and 400 (IV, XL and CD) has been the usual form since Roman times, additive notation to represent these numbers (IIII, XXXX and CCCC)^[9] continued to be used, including in compound numbers like XXIIII,^[10] LXXIIII,^[11] and CCCCLXXXX.^[12] The additive forms for 9, 90, and 900 (VIIII,^[9] LXXXX,^[13] and DCCCC^[14]) have also been used, although less often.

The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to the Colosseum, IIII is systematically used instead of IV, but subtractive notation is used for XL; consequently, gate 44 is labelled XLIIII.^[15][16]

Modern clock faces that use Roman numerals still very often use IIII for four o’clock but IX for nine o’clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.^[17][18][19] However, this is far from universal: for example, the clock on the Palace of Westminster tower (commonly known as Big Ben) uses a subtractive IV for 4 o’clock.^[18]

Isaac Asimov once mentioned an «interesting theory» that Romans avoided using IV because it was the initial letters of IVPITER, the Latin spelling of Jupiter, and might have seemed impious.^[20] He did not say whose theory it was.

Several monumental inscriptions created in the early 20th century use variant forms for «1900» (usually written MCM). These vary from MDCCCCX for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for 1903, on the north entrance to the Saint Louis Art Museum.^[21]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written IIIII and XXXXX instead of V and L, and there are instances such as IIIIII and XXXXXX rather than VI or LX.^[22][23]

Other subtractive forms

There is a common belief that any smaller digit placed to the left of a larger digit is subtracted from the total, and that by clever choices a long Roman numeral can be «compressed». The best known example of this is the ROMAN() function in Microsoft Excel, which can turn 499 into CDXCIX, LDVLIV, XDIX, VDIV, or ID depending on the «Form» setting.^[24] There is no indication this is anything other than an invention by the programmer, and the universal-subtraction belief may be a result of modern users trying to rationalize the syntax of Roman numerals.

There is, however, some historic use of subtractive notation other than that described in the above «standard»: in particular IIIXX for 17,^[25] IIXX for 18,^[26] IIIC for 97,^[27] IIC for 98,^[28][29] and IC for 99.^[30] A possible explanation is that the word for 18 in Latin is duodeviginti, literally «two from twenty», 98 is duodecentum (two from hundred), and 99 is undecentum (one from hundred).^[31] However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.

There are multiple examples of IIX being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than VIII. XIIX was used by officers of the XVIII Roman Legion to write their number.^[32][33] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.^[34]

Rare variants

While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.

• IIXX was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say «twenty-second» in Latin, namely duo et vice(n)sima (literally «two and twentieth») rather than the «regular» vice(n)sima secunda (twenty second).^[35] Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of «22nd Legion» stood for 18, and «corrected» it to XVIII.^[35]

• There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as XVIXIII, corresponding to the common reading «sixteen thirteen» of such year numbers in English, or 1519 as XV^CXIX as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.^[37]
• In some French texts from the 15th century and later one finds constructions like IIII^XXXIX for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen).^[37] Similarly, in some English documents one finds, for example, 77 written as «iii^xxxvii» (which could be read «three-score and seventeen»).^[38]
• A medieval accounting text from 1301 renders numbers like 13,573 as «XIII. M. V. C. III. XX. XIII«, that is, «13×1000 + 5×100 + 3×20 + 13».^[39]
• Other numerals that do not fit the usual patterns – such as VXL for 45, instead of the usual XLV — may be due to scribal errors, or the writer’s lack of familiarity with the system, rather than being genuine variant usage.

Non-numeric combinations

As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, «XXX» and «XL» have other connotations in addition to their values as Roman numerals, while «IXL» more often than not is a gramogram of «I excel», and is in any case not an unambiguous Roman numeral.^[40]

Zero

As a non-positional numeral system, Roman numerals have no «place-keeping» zeros. Furthermore, the system as used by the Romans lacked a numeral for the number zero itself (that is, what remains after 1 is subtracted from 1). The word nulla (the Latin word meaning «none») was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from 525 AD.^[41][42] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for «nothing») for 0, in a table of epacts, all written in Roman numerals.^[43]

The use of N to indicate «none» long survived in the historic apothecaries’ system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.^[44]

Fractions

The base «Roman fraction» is S, indicating 1⁄2.
The use of S (as in VIIS to indicate 71⁄2) is attested in some ancient inscriptions^[45]
and also in the now rare apothecaries’ system (usually in the form SS):^[44] but while Roman numerals for whole numbers are essentially decimal S does not correspond to 5⁄10, as one might expect, but 6⁄12.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 2² × 3) makes it easier to handle the common fractions of 1⁄3 and 1⁄4 than does a system based on ten (10 = 2 × 5). Notation for fractions other than 1⁄2 is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit as. Fractions less than 1⁄2 are indicated by a dot (·) for each uncia «twelfth», the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is S for semis «half». Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine.^[46] The arrangement of the dots was variable and not necessarily linear. Five dots arranged like (⁙) (as on the face of a die) are known as a quincunx, from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.

Each fraction from 1⁄12 to 12⁄12 had a name in Roman times; these corresponded to the names of the related coins:

Other Roman fractional notations included the following:

Large numbers

During the centuries that Roman numerals remained the standard way of writing numbers throughout Europe, there were various extensions to the system designed to indicate larger numbers, none of which were ever standardised.

Apostrophus

One of these was the apostrophus,^[47] in which 500 was written as IↃ, while 1,000 was written as CIↃ.^[20] This is a system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses), which has its origins in Etruscan numeral usage.

Each additional set of C and Ↄ surrounding CIↃ raises the value by a factor of ten: CCIↃↃ represents 10,000 and CCCIↃↃↃ represents 100,000. Similarly, each additional Ↄ to the right of IↃ raises the value by a factor of ten: IↃↃ represents 5,000 and IↃↃↃ represents 50,000. Numerals larger than CCCIↃↃↃ do not occur.^[48]

Sometimes CIↃ was reduced to ↀ for 1,000. Similarly, IↃↃ for 5,000 was reduced to ↁ; CCIↃↃ for 10,000 to ↂ; IↃↃↃ for 50,000 to ↇ (ↇ); and CCCIↃↃↃ (ↈ) for 100,000 to ↈ.
^[49]

IↃ and CIↃ most likely preceded, and subsequently influenced, the adoption of «D» and «M» in Roman numerals.

John Wallis is often credited for introducing the symbol for infinity ⟨∞⟩, and one conjecture is that he based it on ↀ, since 1,000 was hyperbolically used to represent very large numbers.

Vinculum

Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a «bar» or «overline».^[49] It was a common alternative to the apostrophic ↀ during the Imperial era: both systems were in simultaneous use around the Roman world (M for ‘1000’ was not in use until the Medieval period).^[50]
[51]
The use of vinculum for multiples of 1,000 can be observed, for example, on the milestones erected by Roman soldiers along the Antonine Wall in the mid-2nd century AD.^[52] The vinculum for marking 1,000s continued in use in the Middle Ages, though it became known more commonly as titulus.^[53]

Some modern sources describe the vinculum as if it were a part of the current «standard».^[54] However, this is purely hypothetical, since no common modern usage requires numbers larger than the current year (MMXXIII). Nonetheless, here are some examples, to give an idea of how it might be used:

• IV = 4,000
• IVDCXXVII = 4,627
• XXV = 25,000
• XXVCDLIX = 25,459

This use of lines is distinct from the custom, once very common, of adding both underline and overline (or very large serifs) to a Roman numeral, simply to make it clear that it is a number, e.g.
for 1967. There is some scope for confusion when an overline is meant to denote multiples of 1,000, and when not. The Greeks and Romans often overlined letters acting as numerals to highlight them from the general body of the text, without any numerical significance. This stylistic convention was, for example, also in use in the inscriptions of the Antonine Wall,^[55] and the reader is required to decipher the intended meaning of the overline from the context.

Another medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10:^{[citation needed]} thus M for 10,000 as an alternative form for X. In combination with the overline the bracketed forms might be used to raise the multiplier to ten thousand, thus:

• VIII for 80,000
• XX for 200,000

This same syntax may also have indicated multiplication by 100^{[citation needed]} so the above two examples are 800,000 and 2,000,000.

Origin

The system is closely associated with the ancient city-state of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.

Etruscan numerals

Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

The Roman numerals, in particular, are directly derived from the Etruscan number symbols: ⟨𐌠⟩, ⟨𐌡⟩, ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ for 1, 5, 10, 50, and 100 (They had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since Etruscan was written from right to left.)^[56]

The symbols ⟨𐌠⟩ and ⟨𐌡⟩ resembled letters of the Etruscan alphabet, but ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as 𐌠𐌠𐌠𐌢𐌢, 𐌠𐌠𐌢𐌢, and 𐌠𐌢𐌢, mirroring the way they spoke those numbers («three from twenty», etc.); and similarly for 27, 28, 29, 37, 38, etc. However, they did not write 𐌠𐌡 for 4 (nor 𐌢𐌣 for 40), and wrote 𐌡𐌠𐌠, 𐌡𐌠𐌠𐌠 and 𐌡𐌠𐌠𐌠𐌠 for 7, 8, and 9, respectively.^[56]

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: ⟨𐌠⟩, ⟨𐌢⟩, and ⟨𐌟⟩. The symbols for 5 and 50 changed from ⟨𐌡⟩ and ⟨𐌣⟩ to ⟨V⟩ and ⟨ↆ⟩ at some point. The latter had flattened to ⟨⊥⟩ (an inverted T) by the time of Augustus, and soon afterwards became identified with the graphically similar letter ⟨L⟩.^[48]

The symbol for 100 was written variously as ⟨𐌟⟩ or ⟨ↃIC⟩, and was then abbreviated to ⟨Ↄ⟩ or ⟨C⟩, with ⟨C⟩ (which matched the Latin letter C) finally winning out. It might have helped that C was the initial letter of CENTUM, Latin for «hundred».

The numbers 500 and 1000 were denoted by V or X overlaid with a box or circle. Thus 500 was like a Ↄ superimposed on a Þ. It became D or Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified as the letter D; an alternative symbol for «thousand» was a CIↃ, and half of a thousand or «five hundred» is the right half of the symbol, IↃ, and this may have been converted into D.^[20]

The notation for 1000 was a circled or boxed X: Ⓧ, ⊗, ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. Over time, the symbol changed to Ψ and ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille «thousand».^[48]

According to Paul Kayser, the basic numerical symbols were I, X, C and Φ (or ⊕) and the intermediate ones were derived by taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).^[57]

Classical Roman numerals

The Colosseum was constructed in Rome in CE 72–80,^[58] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,^[59] to demonstrate that in Imperial times Roman numerals had already assumed their classical form: as largely standardised in current use. The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation — while XL is used for 40, IV is avoided in favour of IIII: in fact gate 44 is labelled XLIIII.

Use in the Middle Ages and Renaissance

Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: i, ii, iii, iv, and so on.

Since the Middle Ages, a «j» has sometimes been substituted for the final «i» of a «lower-case» Roman numeral, such as «iij» for 3 or «vij» for 7. This «j» can be considered a swash variant of «i«. Into the early 20th century, the use of a final «j» was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.^[60]

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called «medieval Roman numerals». Some simply substitute another letter for the standard one (such as «A» for «V«, or «Q» for «D«), while others serve as abbreviations for compound numerals («O» for «XI«, or «F» for «XL«). Although they are still listed today in some dictionaries, they are long out of use.^[61]

Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient «Arabic» equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

• Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers and are usually read as ordinals; e.g. II is pronounced «the second». This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
• Generational suffixes, particularly in the U.S., for people sharing the same name across generations, for example William Howard Taft IV. These are also usually read as ordinals.
• In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
• The year of production of films, television shows and other works of art within the work itself. Outside reference to the work will use regular Arabic numerals.

• Hour marks on timepieces. In this context, 4 is often written IIII.
• The year of construction on building façades and cornerstones.
• Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
• Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
• Sequels to some films, video games, and other works (as in Rocky II, Grand Theft Auto V).
• Outlines that use numbers to show hierarchical relationships.
• Occurrences of a recurring grand event, for instance:
  • The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad).
  • The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XLII; Super Bowl 50 was a one-time exception^[64]).
  • WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.

Specific disciplines

In astronautics, United States rocket model variants are sometimes designated by Roman numerals, e.g. Titan I, Titan II, Titan III, Saturn I, Saturn V.

In astronomy, the natural satellites or «moons» of the planets are traditionally designated by capital Roman numerals appended to the planet’s name. For example, Titan’s designation is Saturn VI.

In chemistry, Roman numerals are often used to denote the groups of the periodic table. They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.

In education, school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, «grade IX» is sometimes seen for «grade 9».

In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

In graphic design stylised Roman numerals may represent numeric values.

In law, Roman numerals are commonly used to help organize legal codes as part of an alphanumeric outline.

In advanced mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2-era German III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

• Movements are often numbered using Roman numerals.
• In Roman Numeral Analysis, harmonic function is identified using Roman Numerals.
• Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries’ system of measurement: including SS to denote «one half» and N to denote «zero».^[44][65]

In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.

In seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale of earthquakes.

In sport the team containing the «top» players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the «1st XV«, while a lower-ranking cricket or American football team might be the «3rd XI«.

In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.

In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for «seventy»).

Modern use in European languages other than English

Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe and in other regions (e.g. Latin America) that use a European language other than English. For instance:

Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French XVIII^e siècle^[66] and the Spanish siglo XVIII mean «18th century». Slavic languages in and adjacent to Russia similarly favor Roman numerals (xviii век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes «18.» (with a period) before the local word for «century».

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals, while the day is in Arabic numerals: «4.VI.1789″ and «VI.4.1789″ both refer unambiguously to 4 June 1789.

Roman numerals are sometimes used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,^[67] and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is closed on Sundays. Note that the listing uses 24-hour time.

Roman numerals may also be used for floor numbering.^[68][69] For instance, apartments in central Amsterdam are indicated as 138-III, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as 138-huis.

In Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX/17 thus marks 17.9 km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the Italian Parliament from 2018 to 2022 (elected in the 2018 Italian general election) is called the XVIII Legislature of the Italian Republic (or more commonly the «XVIII Legislature»).

A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The «Number Forms» block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.^[70] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that «[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters».^[71]
The block also includes some apostrophus symbols for large numbers, an old variant of «L» (50) similar to the Etruscan character, the Claudian letter «reversed C», etc.

See also

References

Notes

Citations