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Greek Numerals

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Greek Numerals
There are two prominent types of Greek numerals which had been predominately in use over 2000 years ago. The first type was called the Attic numerals which featured about 600 BC and was known as the Ionic numerals developed around 200 BC.

The Attic numerals were an additive system, non-positional, no zeroes was used and the symbols employed were I=1, Γ=5, Δ=10, H=100, Γ =50, Γ =500, X=1000 and M=10,000. Some of these letters are the first letters of the metric prefixes; (deca=10, hecto=100, kilo=1000, and m= myriad, signifying a large number). Since the numbers are not positional, 541 can be written as Γ Δ Δ Δ Δ 1 or Δ Δ 1 Δ Δ Γ . Similarly, 4002 can be written as x x x x 1 1, x 1 x 1 x x, x x x capital gamma symbol(Γ) with the number inserted in it such as Γ would represent 500.

The Ionic symbols which are more recent are similarly additive, non-positional and had no zeroes. The symbols used however were the 24 letters o the Geek alphabet and accent marks or lines were used to differentiate between a word and a numeral. The letters representing numerals from 1 to 9 were:
A Β Γ Δ Ε FΖ Η Θ
1 2 3 4 5 6 7 8 9
The tens were the next nine letters:
Ι Κ Λ Μ Ν Ξ Ο II Q
10 20 30 40 50 60 70 80 90
The hundredts were the next nine letters
P Σ Τ Υ Φ Χ Ψ Ω Ζ
100 200 300 400 500 600 700 800 900 (Newman,1956,p 446 – 447)

The Greeks skilfully utilized the 27 letters of their alphabet making three divisions of nine letters employing the second and third divisions as multiples of ten of the previous numbers. The number 543 can be represented by the symbols ΦΜΓ or ΓΦΜ as it did not matter the position of the symbols. Preceding commas were used to denote thousands up to 9000, and writing below a numeral would indicate multiplying it by 10,000 eg Γ = 30,000 or ΛB = 420,000. By these methods very large numbers could be calculated as by that era the Greek societies was undergoing rapid changes and with the improvement in learning, medicine and industry the population was growing to monumental figures. These developments made the use of an efficient number system more relevant and it was obvious the Greeks at this time had the most advance culture having improved upon the Egyptian and Babylonian civilisations.

However, the Greeks numerals were by no means absolute for there were numerous shortcomings. It was still cumbersome to add or subtract numbers and as zeroes and the decimal were not then in use it meant that it was impossible to have numbers less than 1 or to represent very small numbers such as 0.001432. Also as fractions are less than 1, these could not be used and these impediments would hinder further development in maths and science where the use of minute numbers and fractions are inevitable in calculations.
Bibliography:

NEWMAN R J.(Ed)(1956) The World of Mathematics Vol 1. New York:Dover Publications, Inc.

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