Roman numerals

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Roman numerals are a system of numerical notations used by the Romans. They are an additive (and subtractive) system in which letters are used khổng lồ denote certain "base" numbers, & arbitrary numbers are then denoted using combinations of symbols. Unfortunately, little is known about the origin of the Roman numeral system (Cajori 1993, p.30).

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The following table gives the Latin letters used in Roman numerals và the corresponding numerical values they represent.

characternumerical value
I1
V5
X10
L50
C100
D500
M1000

For example, the number 1732 would be denoted MDCCXXXII in Roman numerals. However, Roman numerals are not a purely additive number system. In particular, instead of using four symbols to lớn represent a 4, 40, 9, 90, etc. (i.e., IIII, XXXX, VIIII, LXXXX, etc.), such numbers are instead denoted by preceding the symbol for 5, 50, 10, 100, etc., with a symbol indicating subtraction. For example, 4 is denoted IV, 9 as IX, 40 as XL, etc. However, this rule is generally not followed on the faces of clocks, where IIII is usually encountered instead of IV. Furthermore, the practice of placing smaller digits before large ones khổng lồ indicate subtraction of value was hardly ever used by Romans and came into popularity in Europe after the invention of the printing press (Wells 1986, p.60; Cajori 1993, p.31).

The following table gives the (Europeanized) Roman numerals for the first few positive integers.

#RN#RN#RN
1I11XI21XXI
2II12XII22XXII
3III13XIII23XXIII
4IV14XIV24XXIV
5V15XV25XXV
6VI16XVI26XXVI
7VII17XVII27XXVII
8VIII18XVIII28XXVIII
9IX19XIX29XXIX
10X20XX30XXX
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For large numbers, the Romans placed a partial frame around numbers (open at the bottom), which indicated that the framed number was to lớn be multiplied by

*
, as illustrated above (Menninger 1992, p.44; Cajori 1993, p.32). In more recent practice, the strokes were sometimes written only on the sides, e.g.,
*
(Cajori 19993, p.32). It should also be noted that the Romans themselves never wrote M for 1000, but instead wrote (I) for
*
, (I)(I) for
*
, etc., and also occasionally wrote IM, IIM, etc. (Menninger 1992, p.281; Cajori 1993, p.32). However, in the Middle Ages, the use of M became quite comtháng. The Romans sometimes used multiple parentheses lớn denote nested multiplications by 10, so (I) for
*
, ((I)) for
*
, (((I))) for
*
, etc. (Cajori 1993, p.33).

The Romans also occasionally used a vinculum (called a titulus in the Middle Ages) over a Roman numeral to indicate multiplication by 1000, so

*
,
*
, etc. (Menninger 1992, p.281; Cajori 1993, p.32).

Roman numerals are encountered in the release year for movies và occasionally on the numerals on the faces of watches and clocks, but in few other modern instances. They vì chưng have sầu the advantage that addition can be done "symbolically" (& without worrying about the "place" of a given digit) by simply combining all the symbols together, grouping, writing groups of five Is as V, groups of two Vs as X, etc.

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The number of characters in the Roman numerals for 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... (i.e., I, II, III, IV, V, VI, VII, VIII, IX, X, ...) are 1, 2, 3, 2, 1, 2, 3, 4, 2, 1, 2, 3, 4, ... (OEIS A006968). This leads to lớn a scale-invariant fractal-lượt thích stairstep pattern which rises in steps then falls abruptly.


REFERENCES:

Cajori, F. A History of Mathematical Notations, 2 vols. Bound as One, Vol.1: Notations in Elementary Mathematics. New York: Dover, pp.30-37, 1993.

Menninger, K. Number Words and Number Symbols: A Cultural History of Numbers. New York: Dover, pp.44-45 và 281, 1992.

Neugebauer, O. TheExact Sciences in Antiquity, 2nd ed. New York: Dover, pp.4-5, 1969.

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Sloane, N.J.A. Sequence A006968/M0417in "The On-Line Encyclopedia of Integer Sequences."

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Villegas, R. "Antique Notations." https://library.hibs.vn.com/infocenter/Demos/4952/.

Wells, D. The Penguin Dictionary of Curious & Interesting Numbers. Middlesex, England: Penguin Books, pp.60 and 79, 1986.

hibs.vn, S. "Mathematical Notation: Past và Future." Transcript of a keynote address presented at MathML & Math on the Web: MathML International Conference 2000. October 20, 2000. https://www.stephenhibs.vn.com/publications/talks/mathml/.


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Weisstein, Eric W. "Roman Numerals." Fromhibs.vn--A hibs.vn Web Resource. https://hibs.vn/RomanNumerals.html


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