Roman Numerals

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

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

For examplethe number 1732 would be denoted MDCCXXXII in Roman numerals. HoweverRoman numerals are not a purely additive number system. In particularinstead of using four symbols to represent a 440990etc. (i.e.IIIIXXXXVIIIILXXXX, etc.)such numbers are instead denoted by preceding the symbol for 55010100, etc.with a symbol indicating subtraction. For example4 is denoted IV, 9 as IX40 as XLetc. Howeverthis rule is generally not followed on the faces of clockswhere IIII is usually encountered instead of IV. Furthermorethe practice of placing smaller digits before large ones to indicate subtraction of value was hardly ever used by Romans and came into popularity in Europe after the invention of the printing press (Wells 1986p. 60; Cajori 1993p. 31).

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

For large numbersthe Romans placed a partial frame around numbers (open at the bottom)which indicated that the framed number was to be multiplied by , as illustrated above (Menninger 1992p. 44; Cajori 1993p. 32). In more recent practicethe strokes were sometimes written only on the sidese.g. (Cajori 19993p. 32). It should also be noted that the Romans themselves never wrote M for 1000but instead wrote (I) for , (I)(I) for , etc.and also occasionally wrote IMIIMetc. (Menninger 1992p. 281; Cajori 1993p. 32). Howeverin the Middle Agesthe use of M became quite common. The Romans sometimes used multiple parentheses to denote nested multiplications by 10so (I) for , ((I)) for , (((I))) for , etc. (Cajori 1993p. 33).

The Romans also occasionally used a vinculum (called a titulus in the Middle Ages) over a Roman numeral to indicate multiplication by 1000so , etc. (Menninger 1992p. 281; Cajori 1993p. 32).

Roman numerals are encountered in the release year for movies and occasionally on the numerals on the faces of watches and clocksbut in few other modern instances. They do have the advantage that addition can be done "symbolically" (and without worrying about the "place" of a given digit) by simply combining all the symbols togethergrouping, writing groups of five Is as Vgroups of two Vs as Xetc.

The Roman numeral corresponding to a Hindu-Arabic number may be obtained in the Wolfram Language using IntegerString[n, "Roman"].

The number of characters in the Roman numerals for 12345678910... (i.e.IIIIIIIVVVIVIIVIIIIXX...) are 1232123, 421234... (OEIS A006968). This leads to a scale-invariant fractal-like stairstep pattern which rises in steps then falls abruptly.