Presentation on theme: "Roman Numerals. Using letters for numbers The Romans depicted numbers using seven letters of the alphabet as numerals I = 1 V = 5 X = 10 L = 50 C = 100."— Presentation transcript:
Using letters for numbers The Romans depicted numbers using seven letters of the alphabet as numerals I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000
Forming numbers Roman numerals are basically strung together to create a total. However the highest possible letter is used at any time. For example VVV = 15 But should be written XV = 15
The subtractive principle The subtractive numeral to the left must be I, X, or C. The 'five' numerals V, L, and D cannot be used. M cannot be used because it is the biggest numeral anyway. So; IV = 4, IX = 9, XL = 40, XC = 90, CM = 900
What can go before what? The subtracted number must be no less than a tenth of the value of the number it is subtracted from. So an X can be placed to the left of a C or an L but not to the left of an M or a D. The correct way of looking at this rule is that each power of ten is dealt with separately. So 49 is XL IX (without the spaces), not IL
Exceptions to the rule Normally, only one smaller number can be placed to the left. So 19 can be depicted XIX but 17 cannot be written XIIIX or IIIXX. However, this rule is sometimes broken for number involving an eight. On some Roman monuments and tombs IIXX for 18 is found. And in recent times times, a statue by Hamo Thornycroft called A Sower in London's Kew Gardens bears an inscription with the date MCMXXIIX meaning 1928. Such uses are not 'correct' but are found very occasionally.
Going to the theatre The Colosseum - constructed between 70 and 80 AD and known as the Flavian Amphitheatre - seated 55,000 people. The audience entered through 80 arches which were numbered 1 to 76 - the four principal entrances were unnumbered. Each spectator had a ticket bearing one of these numbers and entered through the corresponding arch. It is said they could all enter within ten minutes.
Going to the theatre Only 33 doorways remain and they are numbered 23 to 54 with one unnumbered entrance. The numbers do not use the contraction IV or IX. Thus arch 29 is XXVIIII and arch 54 is LIIII. However, the contraction for 40 - XL - is used and so door 44 is XLIIII, as the picture below shows.
Go Large Larger numbers Once a number gets bigger than a few thousand, Roman numerals become unwieldy. There are no 'bigger' symbols for 5000, 10,000 or a million. The Romans had two ways of writing bigger numbers. They used what I call above 'deep parentheses' to multiply a number by 1000. They were a C and a mirror image or upside down C and I use normal parentheses to show them. Thus ( I ) is 1000 and ( X ) is 10,000. ( XXIII ) is 23,000. If you want to depict a million you can use ( M ). Alternatively, the parentheses can be nested so ( I ) is 1,000 and ( ( I ) ) is 1,000,000. The numbers can get a bit unwieldy as they get bigger.
Another way to ‘Go Large’ An alternative way of depicting larger numbers was to put a horizontal bar over the numeral, which multiplied it by 1000. Thus _ V = 5000 and X = 10,000. On a larger scale 3,852,429 can be depicted as ___________ MMMDCCCLMMCDXXIX.
Fractions 1 Fractions The letter S was used to depict a half. Other fractions were shown by dashes, each dash being worth one twelfth. So - meant 1/12, = meant two twelfths which is one sixth, and so on. Twenty three and a half would be written XXIIIS and twelve and a quarter is XII-=. The letter S and the dashes were never used subtractively. Other fractions could not be depicted in Roman numerals.
Fractions 2 - 1/12 S- 1/2 plus 1/12th or 7/12ths = 2/12 or 1/6 S= 1/2 plus 2/12ths or 2/3 -= 3/12ths or 1/4 S-= 1/2 plus 3/12ths or 3/4 == 4/12ths or 1/3 S== 1/2 plus 4/12ths or 5/6 -== 5/12ths S-== 1/2 plus 5/12ths or 11/12ths S 1/2
Zero Zero The Roman numeral system did not include zero and Romans had no concept of it in their arithmetic. Which is one reason why Roman numerals are so clumsy for calculation, though it is possible. They tended to use an abacus for arithmetic and that device does have the concept of zero built in - it is represented by an empty row.
Zero 2 But it was the Indian and Arab mathematicians after the end of the Roman empire who invented our present system where we have the concept of 'place' and have a distinct symbol to represent zero or an empty column. So when we write '10' for example the zero tells us that the '1' is worth ten times as much as it would be if the number was just 1.
Telling the time Draw and complete a clock face with roman numerals What is the difference?