Roman numerals

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Roman numerals on stern of a British clipper ship showing draft in feet. The numbers range from 13 to 22, from bottom to top. CuttySarkRomNum.jpg
Roman numerals on stern of a British clipper ship showing draft in feet. The numbers range from 13 to 22, from bottom to top.

The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, employ seven symbols, each with a fixed integer value, as follows: [1]

Ancient Rome History of Rome from the 8th-century BC to the 5th-century

In historiography, ancient Rome is Roman civilization from the founding of the city of Rome in the 8th century BC to the collapse of the Western Roman Empire in the 5th century AD, encompassing the Roman Kingdom, Roman Republic and Roman Empire until the fall of the western empire. The civilization began as an Italic settlement in the Italian peninsula, dating from the 8th century BC, that grew into the city of Rome and which subsequently gave its name to the empire over which it ruled and to the widespread civilisation the empire developed. The Roman empire expanded to become one of the largest empires in the ancient world, though still ruled from the city, with an estimated 50 to 90 million inhabitants and covering 5.0 million square kilometres at its height in AD 117.

Late Middle Ages period of European history generally comprising the 14th and 15th centuries

The Late Middle Ages or Late Medieval Period was the period of European history lasting from 1250 to 1500 AD. The Late Middle Ages followed the High Middle Ages and preceded the onset of the early modern period.

Latin alphabet alphabet used to write the Latin language (more specific than Q8229: Latin alphabet)

The Latin or Roman alphabet is the writing system originally used by the ancient Romans to write the Latin language. Due to its use in writing Germanic, Romance, and other languages first in Europe and then in other parts of the world and due to its use in Romanizing writing of other languages, it has become widespread. It is also used officially in China and has been adopted by Baltic and some Slavic states. The Latin alphabet evolved from the visually similar Cumaean Greek version of the Greek alphabet, which was itself descended from the Phoenician abjad, which in turn derived from Egyptian hieroglyphics. The Etruscans, who ruled early Rome, adopted the Cumaean Greek alphabet, which was modified over time to become the Etruscan alphabet, which was in turn adopted and further modified by the Romans to produce the Latin alphabet.

Contents

Symbol I V X L C D M
Value1510501005001,000

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 in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.

Roman Empire period of Imperial Rome following the Roman Republic (27 BC–395 AD)

The Roman Empire was the post-Roman Republic period of the ancient Roman civilization. It had a government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, North Africa, and West Asia. From the constitutional reforms of Augustus to the crisis of the third century, the Empire was a principate ruled from the city of Rome. The Roman Empire was then divided between a Western Roman Empire, based in Milan and later Ravenna, and an Eastern Roman Empire, based in Nicomedia and later Constantinople, and it was ruled by multiple emperors.

Arabic numerals ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system, the most common system for the symbolic representation of numbers in the world today

Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; or numerals written using them in the Hindu–Arabic numeral system. It is the most common system for the symbolic representation of numbers in the world today.

Roman numeric system

Basic decimal pattern

The original pattern for Roman numerals used the symbols I, V, and X (1, 5, and 10) as simple tally marks. Each marker for 1 (I) added a unit value up to 5 (V), and was then added to (V) to make the numbers from 6 to 9:

I, II, III, IIII, V, VI, VII, VIII, VIIII, X.

The numerals for 4 (IIII) and 9 (VIIII) proved problematic (among other things, they are easily confused with III and VIII, especially at a quick glance), and are generally replaced with IV (one less than 5) and IX (one less than 10). This feature of Roman numerals is called subtractive notation.

Subtractive notation is an early form of positional notation used with Roman numerals as a shorthand to replace four or five characters in a numeral representing a number with usually just two characters.

The numbers from 1 to 10 (including subtractive notation for 4 and 9) are expressed in Roman numerals as follows:

I, II, III, IV, V, VI, VII, VIII, IX, X. [2]

The system being basically decimal, tens and hundreds follow the same underlying pattern. This is the key to understanding Roman numerals:

Thus 10 to 100 (counting in tens, with X taking the place of I, L taking the place of V and C taking the place of X):

X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C.

Note that 40 (XL) and 90 (XC) follow the same subtractive pattern as 4 and 9, avoiding the confusing XXXX.

Similarly, 100 to 1000 (counting in hundreds):

C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M.

Again - 400 (CD) and 900 (CM) follow the standard subtractive pattern, avoiding CCCC.

In the absence of standard symbols for 5,000 and 10,000 the pattern breaks down at this point - in modern usage M is repeated up to three times. The Romans had several ways to indicate larger numbers, but for practical purposes Roman Numerals for numbers larger than 3,999 are seldom if ever used nowadays, and this suffices.

M, MM, MMM.

Many numbers include hundreds, units and tens. The Roman numeral system being basically decimal, each power of ten is added in descending sequence from left to right, as with Arabic numerals. For example:

As each power of ten (or "place") has its own notation there is no need for place keeping zeros, so "missing places" are ignored, as in Latin (and English) speech, thus:

Roman numerals for large numbers are nowadays seen mainly in the form of year numbers (other uses are detailed later in this article), as in these examples:

Statue of Liberty Colossal neoclassical sculpture on Liberty Island in New York Harbor

The Statue of Liberty is a colossal neoclassical sculpture on Liberty Island in New York Harbor in New York, in the United States. The copper statue, a gift from the people of France to the people of the United States, was designed by French sculptor Frédéric Auguste Bartholdi and its metal framework was built by Gustave Eiffel. The statue was dedicated on October 28, 1886.

<i>The Last Time I Saw Paris</i> 1954 film by Richard Brooks

For the 1942 book, see Elliot Paul.

Enigma (musical project) German band

Enigma is a German musical project founded in 1990 by Romanian-German musician and producer Michael Cretu. Cretu had released several solo records, collaborated with various artists, and produced albums for his then wife, German pop singer Sandra, before he conceived the idea of a New Age, Worldbeat project. He recorded the first Enigma studio album, MCMXC a.D. (1990), with contributions from David Fairstein and Frank Peterson. The album remains Enigma's biggest, helped by the international hit single, "Sadeness ", which sold 12 million units alone. According to Cretu, the inspiration for the creation of the project came from his desire to make a kind of music that did not obey "the old rules and habits" and presented a new form of artistic expression with mystic and experimental components.

A typical clock face with Roman numerals in Bad Salzdetfurth, Germany BadSalzdetfurthBadenburgerStr060529.jpg
A typical clock face with Roman numerals in Bad Salzdetfurth, Germany

Alternative forms

The "standard" forms described above reflect typical modern usage rather than an unchanging and universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval times. There is still no official "binding" standard, which makes the elaborate "rules" used in some sources to distinguish between "correct" and "incorrect" forms highly problematic [7] .

An inscription on Admiralty Arch, London. The number is 1910, for which MCMX would be more usual. AdmiraltyArchLondonCloseup.jpg
An inscription on Admiralty Arch, London. The number is 1910, for which MCMX would be more usual.
Padlock used on the north gate of the Irish town of Athlone. "1613" in the date is rendered XVIXIII, (literally "16, 13."] instead of MDCXIII Padlock, Athlone.jpg
Padlock used on the north gate of the Irish town of Athlone. "1613" in the date is rendered XVIXIII, (literally "16, 13."] instead of MDCXIII

History

Pre-Roman times and ancient Rome

Although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used 𐌠, 𐌡, 𐌢, 𐌣, 𐌚, and for I, V, X, L, C, and M, of which only I and X happened to be letters in their alphabet.

Hypotheses about the origin of Roman numerals

Tally marks

One hypothesis is that the Etrusco-Roman numerals actually derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century. [17]

Thus, I descends not from the letter I but from a notch scored across the stick. Every fifth notch was double cut i.e. , , , , etc.), and every tenth was cross cut (X), IIIIΛIIIIXIIIIΛIIIIXII..., much like European tally marks today. This produced a positional system: Eight on a counting stick was eight tallies, IIIIΛIII, or the eighth of a longer series of tallies; either way, it could be abbreviated ΛIII (or VIII), as the existence of a Λ implies four prior notches. By extension, eighteen was the eighth tally after the first ten, which could be abbreviated X, and so was XΛIII. Likewise, number four on the stick was the I-notch that could be felt just before the cut of the Λ (V), so it could be written as either IIII or (IV). Thus the system was neither additive nor subtractive in its conception, but ordinal . When the tallies were transferred to writing, the marks were easily identified with the existing Roman letters I, V and X. The tenth V or X along the stick received an extra stroke. Thus 50 was written variously as N, И, K, Ψ, , etc., but perhaps most often as a chicken-track shape like a superimposed V and I: . This had flattened to (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter L. Likewise, 100 was variously Ж, , , H, or as any of the symbols for 50 above plus an extra stroke. The form Ж (that is, a superimposed X and I) came to predominate. It was written variously as >I< or ƆIC, was then abbreviated to Ɔ or C, with C variant finally winning out because, as a letter, it stood for centum, Latin for "hundred".

The hundredth V or X was marked with a box or circle. Thus 500 was like a Ɔ superimposed on a or — that is, like a Þ with a cross bar,— becoming 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 bracketed (I) (or CIƆ), and half of a thousand or "five hundred" is the right half of the symbol, I) (or ), and this may have been converted into D. [18] This at least was the etymology given to it later on.

Meanwhile, 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 . The latter symbol further evolved into , then , and eventually changed to M under the influence of the Latin word mille "thousand".

Hand signals

Alfred Hooper has an alternative hypothesis for the origin of the Roman numeral system, for small numbers. [19] Hooper contends that the digits are related to hand gestures for counting. For example, the numbers I, II, III, IIII correspond to the number of fingers held up for another to see. V, then represents that hand upright with fingers together and thumb apart. Numbers 6–10, are represented with two hands as follows (left hand, right hand) 6=(V,I), 7=(V,II), 8=(V,III), 9=(V,IIII), 10=(V,V) and X results from either crossing of the thumbs, or holding both hands up in a cross.

Another possibility is that each I represents a finger and V represents the thumb of one hand. This way the numbers between 1–10 can be counted on one hand using the order: (P=pinky, R=ring, M=middle, I=index, T=thumb N=no fingers/other hand) I=P, II=PR, III=PRM, IV=IT, V=T, VI=TP, VII=TPR, VIII=TPRM, IX=IN, X=N. This pattern can also be continued using the other hand with the fingers representing X and the thumb L.

Intermediate symbols deriving from few original symbols

A third hypothesis about the origins states that the basic ciphers were I, X, C and Φ (or ) and that the intermediary ones were derived from taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D). [20] The Φ was later replaced with M, the initial of mille (the Latin word for "thousand").

Middle Ages and Renaissance

Lower case, 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.

13th century example of iiij. Excerpt from BnF ms. 23112 fr., fol. 343v.png
13th century example of iiij.

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". The use of a final "j" is still used in medical prescriptions to prevent tampering with or misinterpretation of a number after it is written. [21] [22]

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. [23]

NumberMedieval
abbreviation
Notes and etymology
5AResembles an upside-down V. Also said to equal 500.
6ϚEither from a ligature of VI, or from digamma (ϛ), the Greek numeral 6 (sometimes conflated with the stigma ligature). [24]
7S, ZPresumed abbreviation of septem, Latin for 7.
9.5X ̷Scribal abbreviation, an x with a slash through it. Likewise, IX ̷ represented 8.5
11OPresumed abbreviation of onze, French for 11.
40FPresumed abbreviation of English forty.
70SAlso could stand for 7, with the same derivation.
80R
90NPresumed abbreviation of nonaginta, Latin for 90. (N.B. N is also used for "nothing" (nullus)).
150YPossibly derived from the lowercase y's shape.
151KUnusual, origin unknown; also said to stand for 250. [25]
160TPossibly derived from Greek tetra, as 4 × 40 = 160.
200HCould also stand for 2 (see also 𐆙, the symbol for the dupondius). From a barring of two I's.
250E
300B
400P, G
500QRedundant with D; abbreviates quingenti, Latin for 500.
800ΩBorrowed from Gothic.
2000Z

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:

Spanish Real using "IIII" instead of "IV" as regnal number of Charles IV of Spain Carlos IV Coin.jpg
Spanish Real using "IIII" instead of "IV" as regnal number of Charles IV of Spain

Specific disciplines

Entrance to section LII (52) of the Colosseum, with numerals still visible Colosseum-Entrance LII.jpg
Entrance to section LII (52) of the Colosseum, with numerals still visible

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 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:

In pharmacy, Roman numerals are used in some contexts, including S to denote "one half" and N to mean "nothing". [28] (See the sections below on "zero" and "fractions".)

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 cricket or American football team for younger or less experienced players 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 continental Europe

Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe. For instance:

Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French xviiie siècle [29] and the Spanish siglo XVIII mean "18th century". Slavic languages in and adjacent to Russia similarly favour 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".

Boris Yeltsin's signature, dated 10 November 1988. The month is specified by "XI" rather than "11". Yeltsin-authograph-1988.gif
Boris Yeltsin's signature, dated 10 November 1988. The month is specified by "XI" rather than "11".

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: "14.VI.1789" and "VI.14.1789" both refer unambiguously to 14 June 1789.

Business hours table on a shop window in Vilnius DarboLaikas.jpg
Business hours table on a shop window in Vilnius

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, [30] 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.

Sign at 17.9 km on route SS4 Salaria, north of Rome S6002447 cropped.jpg
Sign at 17.9 km on route SS4 Salaria, north of Rome

Roman numerals may also be used for floor numbering. [31] [32] 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 kilometre 17.9.

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.

Special values

Zero

The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval scholars in lieu of 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525. [33] [34] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for "nothing"), in a table of epacts, all written in Roman numerals. [35]

Fractions

A triens
coin (1/3 or 4/12 of an as
). Note the four dots •••• indicating its value. Vecchi 003.jpg
A triens coin (1/3 or 4/12 of an as). Note the four dots •••• indicating its value.
A semis
coin (1/2 or 6/12 of an as
). Note the S indicating its value. Semisse.jpg
A semis coin (1/2 or 6/12 of an as). Note the S indicating its value.

Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because 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). On coins, many of which had values that were duodecimal fractions of the unit as , they used a tally-like notational system based on twelfths and halves. A dot (•) indicated an uncia "twelfth", the source of the English words inch and ounce; dots were repeated for fractions up to five twelfths. Six twelfths (one half) was abbreviated as the letter 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. [36]

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

FractionRoman numeralName (nominative and genitive)Meaning
1/12· Uncia, unciae "Ounce"
2/12 = 1/6·· or : Sextans, sextantis "Sixth"
3/12 = 1/4··· or Quadrans, quadrantis"Quarter"
4/12 = 1/3···· or Triens, trientis"Third"
5/12····· or Quincunx, quincuncis "Five-ounce" (quinque unciaequincunx)
6/12 = 1/2SSemis, semissis"Half"
7/12S·Septunx, septuncis"Seven-ounce" (septem unciaeseptunx)
8/12 = 2/3S·· or S: Bes, bessis "Twice" (as in "twice a third")
9/12 = 3/4S··· or S Dodrans, dodrantis
ornonuncium, nonuncii
"Less a quarter" (de-quadransdodrans)
or "ninth ounce" (nona uncianonuncium)
10/12 = 5/6S···· or S Dextans, dextantis
ordecunx, decuncis
"Less a sixth" (de-sextansdextans)
or "ten ounces" (decem unciaedecunx)
11/12S····· or S Deunx, deuncis"Less an ounce" (de-unciadeunx)
12/12 = 1I As, assis "Unit"

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 .

Other Roman fractional notations included the following:

Large numbers

A number of systems were developed for the expression of larger numbers that cannot be conveniently expressed using the normal seven letter symbols of conventional Roman numerals.

"1630" on the Westerkerk in Amsterdam, with the date expressed in "apostrophus" notation. Westerkerk MDCXXX.jpg
"1630" on the Westerkerk in Amsterdam, with the date expressed in "apostrophus" notation.

Apostrophus

One of these was the apostrophus, [37] in which 500 (usually written as "D") was written as |Ɔ, while 1,000, was written as C|Ɔ instead of "M". [18] This is a system of encasing numbers to denote thousands (imagine the Cs and Ɔs as parentheses), which has its origins in Etruscan numeral usage. The |Ɔ and C|Ɔ used to represent 500 and 1,000 most likely preceded, and subsequently influenced, the adoption of "D" and "M" in conventional Roman numerals.

In this system, an extra Ɔ denoted 500, and multiple extra Ɔs are used to denote 5,000, 50,000, etc. For example:

Base number C|Ɔ = 1,000CC|ƆƆ = 10,000CCC|ƆƆƆ = 100,000
1 extra Ɔ|Ɔ = 500C|ƆƆ = 1,500CC|ƆƆƆ = 10,500CCC|ƆƆƆƆ = 100,500
2 extra Ɔs|ƆƆ = 5,000 CC|ƆƆƆƆ = 15,000CCC|ƆƆƆƆƆ = 105,000
3 extra Ɔs|ƆƆƆ = 50,000  CCC|ƆƆƆƆƆƆ = 150,000

Sometimes C|Ɔ was reduced to ↀ for 1,000. John Wallis is often credited for introducing the symbol for infinity (modern ∞), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, |ƆƆ for 5,000 was reduced to ↁ; CC|ƆƆ for 10,000 to ↂ; |ƆƆƆ for 50,000 to ↇ; and CCC|ƆƆƆ for 100,000 to ↈ. [17]

Page from a 16th-century manual, showing a mixture of apostrophus and vinculum numbers (see in particular the ways of writing 10,000). Roman numerals Bungus 1584-1585.png
Page from a 16th-century manual, showing a mixture of apostrophus and vinculum numbers (see in particular the ways of writing 10,000).

Vinculum

Another system is the vinculum , in which conventional Roman numerals are multiplied by 1,000 by adding an "bar" or "overline". [17] Although mathematical historian David Eugene Smith disputes that this was part of ancient Roman usage, [38] the notation was certainly in use in the Middle Ages, and is sometimes suggested as a workable method for modern use, although it is not standardised as such.

Any hundreds, tens or units in the number are written in ordinary Roman numerals - but instead of M, MM or MMM, "barred" notation is used to express the thousands - which greatly expands the range of numbers expressible.

For instance:

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

If this were ever to be applied consistently in our own times - then the main difficulty would be what to do with "M" - one way would be to do away with "M" altogether, except perhaps for CM (=900) - thus rendering MMXVIII as IIXVIII - or alternatively to retain "M" in its current usage, with the barred numerals starting at IV (=4,000). Retaining "M" would permit our numerals to run up to MMMCMXCIXCMXCIX (= 3,999,999).

Another inconsistent medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10 (or 100): 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 (say) ten (or one hundred) thousand, thus:

  • VIII for 80,000 (or 800,000)
  • XX for 200,000 (or 2,000,000)
Use of Roman numeral "I" (with exaggerated serifs) contrasting with the upper case letter "I". SectionI.JPG
Use of Roman numeral "I" (with exaggerated serifs) contrasting with the upper case letter "I".

Through all this, and whether any kind of vinculum notation or "barring" needs to be revived or not, this needs to be distinguished from the custom, once very common, of adding both underline and overline to a Roman numeral, simply to make it clear that it is a number, e.g. MCMLXVII.

See also

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<i>Liber Abaci</i> Mathematics book published in 1202 by Fibonacci

Liber Abaci is a 1202 historic book on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci.

The plus and minus signs are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction. Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.

Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics. Mathematical notations include relatively simple symbolic representations, such as the numbers 0, 1 and 2; function symbols such as sin; operator symbols such as "+"; conceptual symbols such as lim and dy/dx; equations and variables; and complex diagrammatic notations such as Penrose graphical notation and Coxeter–Dynkin diagrams.

A numerical digit is a single symbol used alone, or in combinations, to represent numbers according to some positional numeral systems. The single digits and their combinations are the numerals of the numeral system they belong to. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.

When used as a diacritic mark, the term dot is usually reserved for the Interpunct, or to the glyphs 'combining dot above' ( ◌̇ ) and 'combining dot below' ( ◌̣ ) which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese.

Positional notation method of representing or encoding numbers

Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude. This greatly simplified arithmetic, leading to the rapid spread of the notation across the world.

The pentimal system is a notation for presenting numbers, usually by inscribing in wood or stone. The notation has been used in Scandinavia, usually in conjunction to runes.

Roman abacus

The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of earlier abacuses like those used by the Greeks and Babylonians. It was the first portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals.

History of the Hindu–Arabic numeral system

The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205".

Hindu–Arabic numeral system positional decimal numeral system

The Hindu–Arabic numeral system is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.

An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In mathematical notation, an overline has been used for a long time as a vinculum, a way of showing that certain symbols belong together. The original use in Ancient Greek was to indicate compositions of Greek letters as Greek numerals. In Latin it indicates Roman numerals multiplied by a thousand and it forms medieval abbreviations (sigla). Marking one or more words with a continuous line above the characters is sometimes called overstriking, though overstriking generally refers to printing one character on top of an already-printed character.

Numeral systems have progressed from the use of tally marks, more than 40,000 years ago, through to the use of sets of glyphs to efficiently represent any conceivable number.

Numerals are characters or sequences of characters that denote a number. The Hindu-Arabic numeral system (base-10) is used widely in various writing systems throughout the world and all share the same semantics for denoting numbers. However, the graphemes representing the numerals differ widely from one writing system to another. To support these grapheme differences, Unicode includes encodings of these numerals within many of the script blocks. The decimal digits are repeated in 22 separate blocks. In addition to many forms of the Hindu-Arabic numerals, Unicode also includes several less common numerals such as: Aegean numerals, Roman numerals, counting rod numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, and also composite characters containing Arabic numerals such as ½.

Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart. The most remarkable of those features is the fact that it is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the Latin alphabet letters for symbols with Arabic letters and the use of Arabic names for functions and relations.

In music, Roman numeral analysis uses Roman numerals to represent chords. The Roman numerals denote scale degrees ; used to represent a chord, they denote the root note on which the chord is built. For instance, III denotes the third degree of a scale or the chord built on it. Generally, uppercase Roman numerals represent major chords while lowercase Roman numerals represent minor chords ; elsewhere, upper-case Roman numerals are used for all chords. In Western classical music in the 2000s, Roman numeral analysis is used by music students and music theorists to analyze the harmony of a song or piece.

References

  1. Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. ISBN   0-520-05079-7. Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.
  2. Reddy, Indra K.; Khan, Mansoor A. (2003). Essential Math and Calculations for Pharmacy Technicians. CRC Press. ISBN   978-0-203-49534-6.
  3. Dela Cruz, M. L. P.; Torres, H. D. (2009). Number Smart Quest for Mastery: Teacher's Edition. Rex Bookstore, Inc. ISBN   9789712352164.
  4. Martelli, Alex; Ascher, David (2002). Python Cookbook. O'Reilly Media Inc. ISBN   978-0-596-00167-4.
  5. "What book is the Statue of Liberty holding? What is its significance?". Quora.
  6. Hayes, David P. "Guide to Roman Numerals". Copyright Registration and Renewal Information Chart and Web Site.
  7. Adams, Cecil (23 February 1990). "What is the proper way to style Roman numerals for the 1990s?". The Straight Dope .
  8. "360:12 tables, 24 chairs, and plenty of chalk". Roman Numerals…not quite so simple.
  9. Asimov, Isaac (1966). Asimov On Numbers (PDF). Pocket Books, a division of Simon & Schuster, Inc. p. 12.
  10. Milham, W.I. (1947). Time & Timekeepers. New York: Macmillan. p. 196.
  11. 1 2 Pickover, Clifford A. (2003), Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, Oxford University Press, p. 282, ISBN   978-0-19-534800-2 .
  12. Adams, Cecil; Zotti, Ed (1988). More of the straight dope. Ballantine Books. p. 154. ISBN   978-0-345-35145-6..
  13. Kennedy, Benjamin H. (1879). Latin grammar. London: Longmans, Green, and Co. p. 150.
  14. Reynolds, Joyce Maire; Spawforth, Anthony J. S. (1996). "numbers, Roman". In Hornblower, Simon; Spawforth, Anthony. Oxford Classical Dictionary (3rd ed.). Oxford University Press. ISBN   0-19-866172-X.
  15. Kennedy, Benjamin Hall (1923). The Revised Latin Primer. London: Longmans, Green & Co.
  16. "Gallery: Museum's North Entrance (1910)". Saint Louis Art Museum. Archived from the original on 4 December 2010. Retrieved 10 January 2014. The inscription over the North Entrance to the Museum reads: "Dedicated to Art and Free to All MDCDIII." These roman numerals translate to 1903, indicating that the engraving was part of the original building designed for the 1904 World's Fair.
  17. 1 2 3 Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk. John Wiley & Sons.
  18. 1 2 Asimov, Isaac (1966). Asimov On Numbers. Pocket Books, a division of Simon & Schuster, Inc. p. 9.
  19. Alfred Hooper. The River Mathematics (New York, H. Holt, 1945).
  20. Keyser, Paul (1988). "The Origin of the Latin Numerals 1 to 1000". American Journal of Archaeology. 92: 529–546. JSTOR   505248.
  21. Sturmer, Julius W. Course in Pharmaceutical and Chemical Arithmetic, 3rd ed. (LaFayette, IN: Burt-Terry-Wilson, 1906). p25. Retrieved 15 March 2010.
  22. Bastedo, Walter A. Materia Medica: Pharmacology, Therapeutics and Prescription Writing for Students and Practitioners, 2nd ed. (Philadelphia, PA: W.B. Saunders, 1919) p582. Retrieved 15 March 2010.
  23. Capelli, A. Dictionary of Latin Abbreviations. 1912.
  24. Perry, David J. Proposal to Add Additional Ancient Roman Characters to UCS Archived 22 June 2011 at the Wayback Machine .
  25. Bang, Jørgen. Fremmedordbog, Berlingske Ordbøger, 1962 (Danish)
  26. Owen, Rob (13 January 2012). "TV Q&A: ABC News, 'Storage Wars' and 'The Big Bang Theory'". Pittsburgh Post-Gazette . Retrieved 13 January 2012.
  27. NFL won't use Roman numerals for Super Bowl 50 Archived 1 December 2015 at the Wayback Machine , National Football League. Retrieved 5 November 2014
  28. Bachenheimer, Bonnie S. (2010). Manual for Pharmacy Technicians. ISBN   1-58528-307-X.
  29. Lexique des règles typographiques en usage à l'imprimerie nationale (in French) (6th ed.). Paris: Imprimerie nationale. March 2011. p. 126. ISBN   978-2-7433-0482-9.On composera en chiffres romains petites capitales les nombres concernant : ↲ 1. Les siècles.
  30. Beginners latin Archived 3 December 2013 at the Wayback Machine , Government of the United Kingdom. Retrieved 1 December 2013
  31. Roman Arithmetic Archived 22 November 2013 at the Wayback Machine , Southwestern Adventist University. Retrieved 1 December 2013
  32. Roman Numerals History Archived 3 December 2013 at the Wayback Machine . Retrieved 1 December 2013
  33. Faith Wallis, trans. Bede: The Reckoning of Time (725), Liverpool, Liverpool Univ. Pr., 2004. ISBN   0-85323-693-3.
  34. Byrhtferth's Enchiridion (1016). Edited by Peter S. Baker and Michael Lapidge. Early English Text Society 1995. ISBN   978-0-19-722416-8.
  35. C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.
  36. Maher, David W.; Makowski, John F., "Literary Evidence for Roman Arithmetic with Fractions Archived August 27, 2013, at the Wayback Machine ", Classical Philology96 (2011): 376–399.
  37. "Merriam-Webster Unabridged Dictionary".
  38. Smith, David Eugene (1958) [1925], History of Mathematics, II, p. 60, ISBN   0-486-20430-8

Sources

Further reading