Mathematics Magazine for Grades 112 





Greek Number Systems There were no single Greek national standards in the first millennium BC. since the various island states prided themselves on their independence. This meant that they each had their own currency, weights and measures etc. These in turn led to small differences in the number system between different states since a major function of a number system in ancient times was to handle business transactions. The first Greek number system we examine is their acrophonic system which was use in the first millennium BC. 'Acrophonic' means that the symbols for the numerals come from the first letter of the number name, so the symbol has come from an abreviation of the word which is used for the number. Here are the symbols for the numbers 5, 10, 100, 1000, 10000.
Now the system was based on the additive principle in a similar way to Roman numerals. This means that 8 is simply V, the symbol for five followed by three symbols for one. Here is 110 in Greek acrophonic numbers.
If base 10 is used with an additive system without intermediate symbols then many characters are required to express certain numbers. The number 9999 would require 36 symbols in such a system and this is very cumbersome. We have already seen that that Greek acrophonic numbers had a special symbol for 5. This is not surprising for it cuts down the characters required and also presumably arises from counting on fingers. We have 10 fingers but there is 5 on each hand. What is slightly more surprising is that the system had intermediate symbols for 50, 500, 5000, and 50000 but they were not new characters, rather they were composite symbols made from 5 and the symbols for 10, 100, 1000, 10000 respectively. Here is how the composites were formed.
 