History of Number Systems: Facts to Know

Babylonians

Wrote in cuneiform (wedge) pattern of writing on soft clay tablets

The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. This form of counting has survived for 4000 years.

Thus, base 60 but the 59 numerals were built with only 2 symbols

Cuneiform numbers were written using a combination of just two signs: a vertical wedge for '1' and a corner wedge for '10'.

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They used no zero

 

Egyptians

The Egyptians had a base 10 system of hieroglyphs for numerals.

There was no symbol for zero

They had seven separate symbols (hieroglyphs) for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million as shown below:

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Greeks

2 systems of numbers

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Within this system the Greeks were the first to show the use of a multiplier by combining symbols like this

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The Greeks also used a numeral system based on the 27 letters in the Greek alphabet. In order to differentiate between numeral and letter, when letters are written to represent numbers, a bar was put over the symbol to distinguish it from the corresponding letter.

 

Incas

The Inca people numbered around 12 million but they were from many different ethnic groups and spoke about 20 different languages. The civilization had reached a high level of sophistication with a remarkable system of roads, agriculture, textile design, and administration. Of course even if writing is not required to achieve this level, counting and recording of numerical information is necessary. Thus, the Incas had developed a method of recording numerical information which did not require writing. It involved knots in strings called quipu. The quipu was not a calculator; rather it was a storage device. Remember that the Incas had no written records and so the quipu played a major role in the administration of the Inca empire since it allowed numerical information to be kept. The quipu consists of strings which were knotted to represent numbers. A number was represented by knots in the string, using a positional base 10 representation. If the number 586 was to be recorded on the string then six touching knots were placed near the free end of the string, a space was left, then eight touching knots for the 10s, another space, and finally 5 touching knots for the 100s.

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Romans

The Romans used 7 symbols to express their number system

character

numerical value

I

1

V

5

X

10

L

50

C

100

D

500

M

1000

 

There was no symbol for zero

The Romans used the idea of subtraction to write numerals. When a smaller numeral is on the left of a larger numeral you take the difference. For example, IV = 5 Ð 1 = 4

Later Romans used a horizontal line above a particular numeral to represent one thousand times that numeral, and additional vertical lines on either side of the numeral to denote one hundred times the number, as in these examples:

 

Indians

They were the first to develop a base ten system. They developed methods of expressing every possible number using a set of ten symbolsÉ very similar to the decimal system we use today with symbols close to the ones we use today.

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Zero was used to denote an empty space.

The scales of measurement used in India are similar to the scales we use today. Example: ÒIndus Inch = 1.32 inches in our system)

 

Mayans

The Mayans discovered/developed zero!

The had a 365 day calendar like ours

The numeral system was base 20. Almost certainly the reason for base 20 arose from ancient people who counted on both their fingers and their toes. Although it was a base 20 system, called a vigesimal system, one can see how five plays a major role, again clearly relating to five fingers and toes. In fact it is worth noting that although the system is base 20 it only has three number symbols (pebble, stick and shell). The shell represented zero as a place holder and as a quantity

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Arabic

The Indian numerals form the basis of the European number systems which are now widely used. However they were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe. The story of this transmission is not, however, a simple one. The eastern and western parts of the Arabic world both saw separate developments of Indian numerals with relatively little interaction between the two. By the western part of the Arabic world we mean the regions comprising mainly North Africa and Spain. Transmission to Europe came through this western Arabic route, coming into Europe first through Spain.

The form of the numerals in the west of the Arabic empire look more familiar to those using European numerals today which is not surprising since it is from these numerals that the Indian number system reached Europe.

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