ROMAN AND MAYAN NUMERATION
Roman numerals were devised by the Roman people to enable counting and perform simple arithmetic calculations in daily life. They used letters to symbolize numbers. With the combination of those letters, any number can be formed.
They are an additive number system. The intermediate values of the numbers are achieved by adding the splitting the given number in terms of the numbers in above table and representing them with alphabets.
Eg.36.
36 can be split as 10+10+10+5+1
So, having the table as reference, it is written as XXXVI.
Similarly, a number 675 can be split as 500+100+50+10+10+5
But the system was not a purely additive one. It was subtractive as well. It was for the numbers where five characters would have been used just to represent a digit.
For eg. to represent 9, by additive form it would have been
VIIII.
We use five characters just to represent the digit 9.
The Romans ,in such cases, used subtractive method.
They denoted subtraction by placing the number to be subtracted before the base numeral.
They denoted 9 as IX
Similarly 4 was represented as IV,90 as XC,400 as CD etc.
For a number 976, the roman numeral representation would be:
900+70+6
ie. CMLXXVI.
For denoting very large numbers, they used a frame around the numbers. It was then replaced with strokes in the middle ages.
or |I| represented 100,000
Similarly |X| represents 1,000,000
In fact,they hardly used M. Instead they represented 1000 as (I) or . To denote 10,000 they used ((I)) or (X). The number of curly brackets signified the number of 10s to be multiplied to the number in bracket.
Eg. to denote 10678,
They use, (X)DCLXXVIII
MAYAN NUMERATION:
The Mayan method of numeration was completely a different one. They did not have an additive type of number system. They instead used only three symbols to represent their numbers. They follow base 20 in their representation.
They used a combination of three symbols to represent their numbers. The above table gives their numbers and their corresponding value. A single dot represents 1.Similarly 2 dots represent 2 and so on up to 4. A horizontal line represents 5. Just as the dots, the number of horizontal lines denotes the multiple of 5. Two horizontal lines denote 10. Three horizontal lines denote 15. The maximum digit represented is 19. It is represented by
The place value of the numbers were 1,20,202 etc. from right to left. To represent bigger numbers, we split the numbers into their corresponding base values and write the symbols in a vertical fashion.
For eg. To denote a number 203,
We split it as 20*10+3*1
So, its representation becomes,
Similarly, we can denote other numbers.
This method was is practice for some years. But after a period of time, the Mayan syatem underwent a slight change.
The first place remained a multiple of 1 and the second place remained a multiple of 20 but the third place became 18*20 instead of 20*20.The fourth place was therefore a multiple of 18*20*20 instead of 20*20*20. This applies to all the places beyond 3.
Eg. A number with a notation as shown,
The value of the number is:
1*(18*20)=360
10*20=200
3*1=3
Adding them up, we get,
360+200+3=563
REFERENCES
- Pickover, Clifford A. (2003), Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, Oxford University Press, p. 282, ISBN 9780195348002.
- Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8
- Thompson, J. Eric S. (1971). Maya Hieroglyphic Writing; An Introduction. Civilization of the American Indian Series, No. 56 (3rd ed.). Norman: University of Oklahoma Press. ISBN 0-8061-0447-3. OCLC 275252
- "numerals and numeral systems". Encyclopædia Britannica. Encyclopædia Britannica Online.Encyclopædia Britannica Inc., 2014. Web. 30 Nov. 2014<http://www.britannica.com/EBchecked/topic/682032/numerals-and-numeral-systems/233814/Roman-numerals>
