ROMAN NUMERALS

My short LoveMaths text this time is about Roman numerals. Roman numerals are very interesting for many historical and cultural reasons, and it is a pity that they have such limited use today and are almost forgotten.

Roman numerals are the numbers that the ancient Romans used. This is just a short reminder about these beautiful numerals, which are still very much alive on some occasions, although they have limited and more specific uses.

One of their greatest disadvantages is that they form very long strings of letters.

Rome was the capital of the vast Roman Empire, which encompassed almost the entire continent of Europe, along with Mediterranean territories in Asia and Africa.

The Roman Empire was one of the most powerful empires of the ancient world. Historians believe that the earliest Roman settlements began in 753 BC.

The Roman Empire was divided into the Western Empire and the Eastern Empire. Its glory reached its peak around AD 200, and the entire empire covered an area of about 2.5 million square miles.

The Romans will forever be remembered as inventors and pioneers: inventors of a modern form of administration and pioneers of a number of scientific and engineering practices that had existed before but were introduced into everyday use by them.

The Romans were extremely innovative builders and engineers. They invented aqueducts, paved roads and advanced drainage systems.

Architecture, science, popular culture, law and government, arts and literature—all of these were highly developed in ancient Rome.

Did you know that the Romans even founded London? They named it Londinium.

The Romans even invented their own numeral system based on the symbols of the Latin alphabet. We call these numerals Roman numerals.

It was the main way of writing numbers throughout Europe until the Late Middle Ages.

Numbers in this system are represented by combinations of letters from the Latin alphabet.

There are seven main symbols, each with a fixed integer value:

Symbol: I, V, X, L, C, D, M

Value: 1, 5, 10, 50, 100, 500, 1000

That means:

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.

These basic symbols can be combined like this:

I = 1, II = 2, III = 3, IV = 4, V = 5, VI = 6, VII = 7, VIII = 8, IX = 9, X = 10, XI = 11, XII = 12, XIII = 13, XIV = 14, XV = 15, XVI = 16, XVII = 17, XVIII = 18, XIX = 19, XX = 20, XXX = 30, XXXI = 31, XXXVIII = 38, XXXIX = 39, XL = 40, L = 50, LX = 60, LXX = 70, LXXX = 80, XC = 90, C = 100, CC = 200, CCC = 300, CD = 400, D = 500, DC = 600, DCC = 700, DCCC = 800, CM = 900, M = 1000.

There are some rules for forming numbers:

When a symbol appears after a larger (or equal) symbol, it is added.

Example: VI = V + I = 5 + 1 = 6

Example: LXX = L + X + X = 50 + 10 + 10 = 70

But if a symbol appears before a larger symbol, it is subtracted.

Example: IV = V − I = 5 − 1 = 4

Example: IX = X − I = 10 − 1 = 9

A practical rule to remember is: After a larger symbol, it is added!

Do not use the same symbol more than three times in a row (although IIII is sometimes used for 4, particularly on clocks).

Numbers greater than 1,000 are formed by placing a bar over the symbol, meaning "times 1,000", but this notation is not commonly used.

The use of Roman numerals continued long after the decline of the Roman Empire.

From the 14th century onwards, they 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 specialised applications to this day.

The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval scholars.

Around AD 725, Saint Bede, or one of his colleagues, used the letter N, the initial of nulla or nihil, in a table of calendars written entirely in Roman numerals.

There is not, and never has been, an official or universally accepted standard for Roman numerals.

Usage in ancient Rome varied greatly and remained inconsistent during the Middle Ages and later.

The "rules" of the system as it is used today have developed gradually through centuries of common usage.

Roman numerals are essentially a decimal, or "base 10", number system, in which the powers of ten—thousands, hundreds, tens and units—are written separately from left to right in that order.

In the absence of place-value zeros, different symbols are used for each power of ten, but a common pattern is followed for each of them.

Here are some examples of larger numbers written in Roman numerals:

• 39 = 30 + 9 = XXX + IX = XXXIX
• 246 = 200 + 40 + 6 = CC + XL + VI = CCXLVI
• 789 = 700 + 80 + 9 = DCC + LXXX + IX = DCCLXXXIX
• 2,421 = 2,000 + 400 + 20 + 1 = MM + CD + XX + I = MMCDXXI
• 160 = 100 + 60 = C + LX = CLX
• 207 = 200 + 7 = CC + VII = CCVII
• 1,009 = 1,000 + 9 = M + IX = MIX
• 1,066 = 1,000 + 60 + 6 = M + LX + VI = MLXVI

Roman numerals for large numbers are nowadays seen mainly in the form of years, as in these examples:

• 1776 = 1,000 + 700 + 70 + 6 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty)
• 1954 = 1,000 + 900 + 50 + 4 = M + CM + L + IV = MCMLIV (as shown in the trailer for the film The Last Time I Saw Paris)
• 2014 = 2,000 + 10 + 4 = MM + X + IV = MMXIV (the year of the XXII (22nd) Olympic Winter Games in Sochi, Russia)
• The current year (2020) is MMXX.

The largest number that can be represented in this notation is 3,999 (3,000 + 900 + 90 + 9 = MMM + CM + XC + IX = MMMCMXCIX).

The Roman numeral system was developed around 500 BC.

As the Romans conquered much of the world known to them, their numeral system spread throughout Europe, where Roman numerals remained the primary way of representing numbers for centuries.

Around AD 1300, Roman numerals were replaced throughout most of Europe by the more efficient Hindu-Arabic numeral system that is still used today.

Today, Roman numerals are often used for ceremonial or decorative purposes. Sometimes they give an air of formality that Hindu-Arabic numerals do not.

Roman numerals are still used today and can be found in many places:

• On clock faces. For example, 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 and XII.
• On buildings, where the year of construction may be written in Roman numerals.
• On the reverse of the Great Seal of the United States, where the pyramid bears the inscription MDCCLXXVI, the date of American independence.
• In the copyright dates of films and television programmes shown during the end credits.
• In outline documents, where Roman numerals are often used for the highest level of headings.
• In some older books, especially for chapter or part numbers.
• As page numbers in the front matter of books (Preface, Foreword, Contents, etc.), allowing the main text to begin with page 1 in Hindu-Arabic numerals.
• In the names of popes, kings and queens, for example Pope Gregory XIII and King George III.
• In people's names where sons are named after their fathers, for example John Smith II and John Smith III.
• In Roman and Slavic languages to denote centuries, for example the XVIII century (18th century).

• Here are some activities for you involving Roman numerals. The tasks are about converting Roman numerals into Arabic numerals and converting Arabic numerals into Roman numerals.

  Activity 1: Can you write the following numbers in Roman numerals?

  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100, 500, 1000.

  Activity 2: Can you write the following Roman numerals using Arabic numerals?

  I, II, III, IV, V, VI, VII, VIII, IX, X, XX, XXX, XXXX, L, C, D, M.

  Activity 3: Convert 1984 into Roman numerals.

  Here is a little clue:

  1000 = M

  900 = CM (because M − C = 1000 − 100 = 900)

  80 = LXXX

  4 = IV

  Now put them together.

  Can you describe the occasions in your life when you use Roman numerals?

  Practise this beautiful and fascinating language of Roman numerals!

  You can even impress some of your friends by sending them messages that include numbers written in Roman numerals. They will be proud to have such intelligent friends!

  Stay cool and love knowledge!

  (Day XXX, Month IV, Year MMXX)

  (E. S. Lyubenova; LoveMaths Story for My Students)