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Greek numbers

Ancient Greece is undoubtedly one of the richest and most fascinating civilizations in the history of mankind. Thousands of scholars have stopped to analyze their art, their political system or the great contributions they made in ethical and philosophical matters. However, in this case we are going to stop to know a little more about your numeral system, that is, the Greek numbers.

ancient greek

The Greek numbering system was uniquely based upon their alphabet. The Greek alphabet came from the Phoenicians around 900 B.C. When the Phoenicians invented the alphabet, it contained about 600 symbols.

who invented the greek number system?

The Greeks used the Ionic system until the incorporation of the Arabic number system that replaced it (and which is what we use today).

The Greek number system does not present much more difficulties than learning the values ​​of the 27 letters and the minimum rules used to represent any number.




it is estimated that the oldest Greek numbering system was the so-called attic or acroponic, which worked similarly to the Roman, which derives from this system. It is estimated that it appeared around the sixth century BC. C. From the fourth century a. C., the acrophonic system is replaced by a quasi-decimal alphabetic system, called an Ionic.


There's an exemple of how they add to make big numbers with attic system

This numerical system of the Greeks, known as Ionic, consisted in assigning a letter to each unit figure, to each ten another letter and to each hundred, another letter. This implied the requirement of 27 letters, so that the Greek system of 24 letters was extended, with three letters already outdated: the digamma calls for the 6 (today stigma is used), qoppa for the 90 (nowadays the numerical qoppa), and sampi for the 900. To distinguish the numbers of the letters, we place a sharp accent at the end of each group. The alphabetic or Ionian system is based on the principle of the sum in which the numerical values ​​of the letters are added to form the total. For example, 241 is represented as σμα´ (200 + 40 + 1).


Finally, it is important to highlight an important element within the Greek numerical system: the Hellenistic zero. The notion of «zero2 is undoubtedly one of the most curious concepts in the oldest number systems, and in the Greek case it is not an exception, although this civilization already had the advances that the Egyptians or the PhoeniciansHellenistic astronomers included a special symbol for 0. This zero was used more often in the representation of figures. Examples of this were the limitation of fractions, called minutes, seconds, thirds, quarters, etc .; not being used in the whole part of a number.

Helenistic zero

  • As we have already pointed out, in the Greek numbering each letter of the alphabet represented a number from 1 to 9. If you wanted to add more figures, it was done by means of the next nine letters of the alphabet, so to complete the 27 available characters. This fact, joining numbers to letters of the alphabet, caused certain numbers to be formed by a combination of letters that formed words with esoteric and mysterious dyes. In other words, the Greek numbering system also had its influence on the fears and superstitions of the people of the time.


2n - 1 (2n-1) = N

  • The Greeks were one of the first civilizations that sought the perfect number. The perfect numbers are those in which the results of all possible divisions would add the number itself. That is, the results of the possible divisions of the number 28 would be 14, 7, 4, 2 and 1. When adding these figures (the results of their possible divisions) we get the number itself, 28. Although it seems simple, few numbers They comply. The first is 1, the second the 6, the third the 28, the fourth the 496, the fifth the 8,128 and the sixth would already be 33,550,336. The formula for finding the perfect numbers is 2n-1 (2n-1) = N.
  • Although the Greek civilization was distinguished by its great thinkers and its advances in political, social or philosophical issues, the Greek numeral system accused of excessive rigidity that did nothing practical to perform arithmetic calculations. Therefore, the Greek civilization is not characterized mainly by its contributions in mathematical matters, although there are always exceptions.