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 not fair that they have a limited use and are almost forgotten. Roman Numerals are the numbers that ancient Romans used. This is just a short reminder about these beautiful numerals, which are still very much alive in some occasions although with some limited and more specific uses. One of the greatest disadvantages is that they form a very big chain of letters.

Rome was the capital of the expansive 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 was at its peak in 200 AD, and the entire empire spanned over an area of 2.5 million square miles. Romans will forever be remembered as inventors and establishers: inventors of a modern form of administration and establishers of a number of science and engineering practices which had been around, but were ushered in for daily use by them. The Romans were extremely innovative builders and engineers (they invented the aqueducts, the paved roads, and the construction of the drains). Architecture, Science, Popular culture, Law and Governance, Arts and Literature - all this was highly developed in ancient Rome. Did you know that the Romans founded even London? They had named it ‘Londinium’.

 Romans even invented their own numeral system based on the symbols of Latin letters. We call these numerals Roman numerals. It was the main way of writing numbers in the whole European continent until the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. There are main seven 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, 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 when forming the 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 the symbol appears before a larger symbol it is subtracted:

• Example: IV = V − I = 5 − 1 = 4
• Example: IX = X − I = 10 − 1 = 9

The practical rule for this is: To Remember: After Larger is Added! Don't use the same symbol more than three times in a row (but IIII is sometimes used for 4, particularly on clocks). Numbers greater than 1,000 are formed by placing a dash over the symbol, meaning "times 1,000", but these are not commonly used.

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century 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 minor 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. About 725, Saint Bede or one of his colleagues used the letter N, the initial of nulla or of nihil , in a table of calendars, all written 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 in medieval times and later. The "rules" of the system as it is now applied have been established only by general usage over the centuries.

Roman numerals are essentially a decimal or "base 10" number system, in that the powers of ten – thousands, hundreds, tens and units – are written separately, from left to right, in that order. In the absence of "place keeping" zeros, different symbols are used for each power of ten, but a common pattern is used for each of them.

Here are some examples for large numbers written with 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 = 2000 + 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 year numbers, 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 in the trailer for the movie The Last Time I Saw Paris)
• 2014 = 2,000 + 10 + 4 = MM + X + IV = MMXIV (the year of the games 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 for representing numbers was developed around 500 b.c. As the Romans conquered much of the world that was known to them, their numeral system spread throughout Europe, where Roman numerals remained the primary manner for representing numbers for centuries. Around a.d. 1300, Roman numerals were replaced throughout most of Europe with the more effective Hindu-Arabic system still used today.

Today Roman numerals are often used for ceremonial or “decorative” purposes; sometimes Roman numerals give an air of formality that Hindu-Arabic numerals don’t.

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

• One place they are often seen is 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, XII.
• On buildings, where the year of construction may be indicated in Roman numerals.
• The reverse of the Great Seal of the United States shows a pyramid that reads “MDCCLXXVI”, the date of American independence.
• It is customary, for some reason, to show copyright dates of movies and TV shows in Roman numerals during the credits.
• In “outline” documents, where Roman numerals are often used as the highest heading level.
• In some older books especially, Roman numerals are used for chapter or part numbers.
• Lowercase Roman numerals are often used as page numbers for “front matter” of books (Preface, Foreword, Contents, etc.), so that the “main” part of the book starts on page 1 with Hindu-Arabic numerals.
• Names of popes, kings, and queens: e.g. Pope Gregory XIII, King George III
• Ordinary peoples’ names, where there is a tradition of boys being named after the father. For example: John Smith names a son after himself, who is then John Smith Jr. or John Smith II. The son then does likewise, and his son is named John Smith III, etc.
• Roman numerals are widely used in Roman and Slavic languages to denote centuries, e.g. XVIII century = 18th century.

Here are some activities for you including Roman numerals. The tasks are about converting/translating some Roman numerals into Arabic numerals and converting/translating some Arabic numerals into Roman numerals.

Activity 1: Can you write the following numbers with Roman numerals? The numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100, 500, 1000.

Activity 2: Can you write with Arabic numbers the following Roman numerals: I, II, III, IV, V, VI, VII, VIII, IX, X, XX, XXX, XXXX, L, C, D, M?

Activity 3: Convert 1984 to Roman numerals. I will give you a little clue: 1000 = M, 900 = CM (because M - C = 1000 - 100 = 900), 80 = LXXX, 4 = IV. You put them together.

Can you describe in which occasions in your life you use Roman numerals?

Practise this beautiful, cool language of Roman numerals! You can impress some of your friends by texting them some numbers with Roman numerals. They will be so 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)