Ionic Numeral System Website Links For
Greek 		 

Information About

Ionic Numeral System
  CATEGORIES ABOUT GREEK NUMERALS
   
numeration
   
SHOPPER'S DELIGHT
 
Shop For:  
Department
Price Minimum:
Price Maximum:
      



Greek numerals are a System Of Representing Numbers using letters of the Greek Alphabet . They are also known by the names ''Milesian numerals'', ''Alexandrian numerals'', or ''alphabetic numerals''. In modern Greece , they are still in use for Ordinal Number s, and in much the same situations as Roman Numerals are in the West; for ordinary ( Cardinal ) numbers, Arabic Numerals are used.

The earliest system of numerals in Greek were the Acrophonic Attic Numerals , operating much like Roman numerals (which derived from this scheme), with the following formula: Ι = 1, Π = 5, Δ = 10, ΠΔ = 50, Η = 100, ΠΗ = 500, Χ = 1000, ΠΧ = 5000, Μ = 10000 and ΠΜ = 50000.

Starting in the (ϝ, also used are Stigma ϛ or στ) for 6, Qoppa (ϟ) for 90, and Sampi (ϡ) for 900. See Numerals: Stigma, Koppa, Sampi . A trailing acute sign (´) is used to distinguish numerals from letters.

The Alphabetic System operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 241 is represented as σμα´ (200 + 40 + 1).

To represent numbers from 1,000 to 999,999 the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. A comma or inverted acute is put in front of thousands to distinguish them from the standard use. For example, 2006 is represented as ,βϛ´ (2000 + 6).

In modern Greece, uppercase letters are preferred, as in Φιλιππος Β΄= Philip II .


HIGHER NUMBERS

The Greeks also used the Myriad to denote 10,000 and the myriad myriad for one hundred million. In his text The Sand Reckoner the natural philosopher Archimedes proposed advanced ways to name very high numbers, such as the number of grains of sand on a beach, and the number of grains of sand on all the beaches on all the worlds in the universe.


HELLENISTIC ZERO

Hellenistic Astronomer s extended this into a Sexagesimal Positional Numbering System by limiting each position to a maximum value of 50 + 9 and including a special symbol for Zero , which was also used alone like our modern zero, more than as a simple placeholder. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.)—they were not used for the Integral part of a number. This system was probably adapted from Babylonian Numerals by Hipparchus c. 140 BC . It was then used by Ptolemy (c. 140 ), Theon (c. 380 ), and Theon's daughter Hypatia (died 415 ).

The Greek sexagesimal place holder or zero symbol changed over time. The symbol used on Papyri during the Second Century was a very small circle with an overbar several diameters long, terminated or not at both ends in various ways. Later, the overbar shortened to only one diameter, similar to our modern o macron (ō), which was still being used in late medieval Arabic manuscripts whenever alphabetic numerals were used. But the overbar was omitted in Byzantine manuscripts, leaving a bare ο (omicron). This gradual change from an invented symbol to ο does not support the hypothesis that the latter was the initial of ουδεν meaning "nothing". Neugebauer, ''The Exact Sciences in Antiquity'' (second edition, Providence, RI: Brown University Press, 1957) 13-14, plate 2.