A numeral is a symbol or collection of symbols that represents a number. A variety of numeration systems developed along with early civilizations. The symbols "3" and "III" are different numerals representing the same number. Ancient cultural systems developed different ways to represent numbers. Our present decimal system is a base 10 system. Other numeration systems developed with bases of 60, 20, 2, etc. Read on for a brief explanation of some of these ancient numeration systems. ROMAN NUMERATION SYSTEM I 1 V 5 X 10 L 50 C 100 D 500 M 1,000 The Roman system is still used today—on faces of clocks, for copyright dates on films and TV shows and on cornerstones of buildings. Roman numerals are written by combining the seven symbols shown on the above chart. Roman numerals are written from left to right. This system uses the principle of addition as well as that of subtraction. A smaller numeral after a larger indicates the smaller is added to the larger; a smaller numeral before a larger one indicates the smaller numeral is subtracted from the larger one. Six is written VI, and four is written IV. Only the numbers 1, 10 and 100 were allowed to be subtracted, and these only from numbers not more than two steps larger. For example, the number I could be subtracted from V to give IV=4, or from X to give IX=9, but could not be subtracted from C or L. Some examples: LXVII=67 XCIX=99 MCMLXXXIV=1984 EGYPTIAN NUMERATION SYSTEM The Egyptians had a base 10 system of hieroglyphics for their numerals. This means that they had separate symbols for one, ten, a hundred, a thousand, ten thousand, one hundred thousand and one million. The Egyptian system was additive; the values of the symbols were added to obtain the number represented. When the "tally" marks reached 10, the symbol for 10 was used. The Egyptians wrote their numbers from right to left, or from left to right. This system was not a positional one. Thus, the number 33 could be represented by: or by: . BABYLONIAN NUMERATION SYSTEM The Babylonian numerals were developed from the Sumerian and Akkadian systems. These numerals were simply wedge marks in clay. This system was essentially a positional base 60 system with some vestiges of a base 10 system within it. A vertical wedge symbol represented 1, and a horizontal wedge symbol represented 10. Spacing was critical in this system. For example, to represent the number 2, the two wedges touch, as seen in the chart. To represent the number 602, there would be a space between the symbols: The far left horizontal wedge represents 10 groups of 60 (10 x 60=600). The two vertical wedges represent the number 2. (600 + 2=602) The number 83 would be represented as: The far left vertical wedge represents 1 group of 60, and the two horizontal wedges with the three vertical wedges represent 23. (60 + 23=83) The base 60 system they developed helped the Babylonians to measure time and the distance around a circle. Our degree-minute-second system of measuring angles stems from the Babylonian division of a circle into 360 equal parts. We still use the base 60 system to measure time as well. MAYAN NUMERATION SYSTEM The ancient Mayans and other Pre-Columbian Mesoamericans developed a mathematical system that used three symbols: a dot (worth 1), a bar (worth 5), and the zero symbolized by a shell. (See table above.) This system was a positional one based on twenties, possibly from ancient people who counted on both their fingers and toes. The concept of five plays a major role in this system. The Mayan system was also additive. When the Mayans wanted to represent a number higher than 20, they displayed the symbols in rows. In this positional vertical writing system, the bars are placed horizontally and the dots go on top of them. For the numeral 61: The top three dots represent 3 groups of 20. (3 x 20=60) The lower dot represents 1. (60 + 1=61) For the numeral 122: The bar with the dot above it represents 6 groups of 20. (6 x 20=120) The dots below the bar represent 2. (120 + 2 =122) Why do you think such different numeration systems emerged? What do you think of these numeration systems? What similarities or differences do you notice between these systems? Which system would you prefer if you had to choose? Can you see any advantages or disadvantages to such numeration systems? Discussion and comments are welcome!! (5 pts. extra credit)

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