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HOW NUMERATION SYSTEMS BEGAN


 

Primitive people had several ways of recording the few numbers they needed. A shepherd could collect pebbles to represent the number of sheep in a flock. Each pebble meant one sheep. A bag of pebbles stood for th e whole flock. By matching the pebbles against the flock, the shepherd could see if any sheep were missing. Mathematicians call this kind of matching one-to-one correspondence.

Later, people developed other ways to record the number of possessions they owned. They tied knots in a leather thong or scratched tally marks on the side of a rock. They then matched the knots or marks against each item.

Then people began to use words to represent numbers. These words described "how many" and helped peopl e to match items mentally. For example, people used the word for "wings" to mean two objects. To refer to four things, they used the name of a fruit that grew in clusters of four. For five items, the word that meant "hand" was used. Such number-names appeared in various primitive languages. They showed that people had begun to form ideas of numbers. Whether they had three fish, three pebbles, or three tally marks, they recognized a "threeness" about each of these groups.

Finally, people began to count by arranging number-names in a certain order. To count, they spoke or wrote the word that meant "one," next the word for "two," then the word for "three," and so on. In time, people in many parts of the world developed various kinds of counting systems. Some were based on five, others on ten, and still others on twelve or sixty. We still use such measures as 12 inches in a foot and 60 minutes in an hour, taken from these ancient systems.

In most early numeration systems, people formed numerals simply by repeating basic symbols and adding their values to get the number they wanted. The Egyptians, Greeks, and Romans used numeral systems of this kind. The Hindus used a numeration system superior to all others. It followed the principle of place value and used a symbol that meant not any. This system became the decimal numeral system, now used in most parts of the world.

 

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