# Counting with Greek Numbers

## Count with Greek numbers

The ancient Greeks originally had a number system like the Romans, but in the 4th century BC, they started using this system. It was a number system closer to Arabic numbers (our own number system). Instead of counting I, II, III like the Egyptians or the Romans, they had different symbols for 1,2,3 up to 9, just like us. However, they did not use the same symbols to represent numbers greater than 9. They had a new set of symbols for 10, 20, 30, and so on, and yet another set for 100, 200, 300. This has the disadvantage, like so many of the ancient counting systems, that you eventually ran out of symbols!

#### How Greek numbers worked

The symbols that the Greeks used were their letters. They are listed below with their sounds. Unfortunately, this method of counting needs 27 letters, and there were only 24 in the Classical Greek alphabet. This meant that the Greeks had to find 3 extra symbols for the missing numbers of 6, 90 and 900. They used 3 archaic letters, which used to be in the alphabet but had been dropped as they were no longer required.

Arabic number Greek number Greek name Sound Arabic number Greek number Greek name Sound Arabic number 1 2 3 4 5 6 7 8 9         alpha beta gamma delta epsilon digamma zeta eta theta a b g d short e z long e th 10 20 30 40 50 60 70 80 90         iota kappa lambda mu nu xi omicron pi koppa i k/c l m n x short o p 100 200 300 400 500 600 700 800 900         rho sigma tau upsilon phi chi psi omega sampi r s t u f/ph ch ps long o

The Greeks did not have a zero. They didn’t need one. If you don’t have any tens value, then you don’t use one of the tens letters.

This system is hard for arithmetic. Not only do you have to learn that alpha + alpha = beta, you also have to learn that iota + iota = kappa and rho + rho = sigma. What a lot of symbols to keep track of! It’s much easier to say 1 + 1 = 2 and 10 + 10 = 20, and 100 + 100 = 200. Multiplication in the Greek system was even worse. They would have to use abacuses for arithmetic.

#### Giving words numerical values

One effect of using letters as numbers was that when you looked at a word, it could look like a number instead. The Greeks (and the Hebrews, who had a similar counting system) enjoyed doing this. My name is Joanna. There is no J in the Greek alphabet, so I would use iota instead. There are two types of O, so I would use omega, the long O. So my name would be      But this has numeric value of 10 + 800 + 1 + 50 + 50 + 1 = 912. In the Book of Revelations, it says “Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.” There have been various suggestions as to what the name might be that would produce the value of 666 – Emperor Nero is an obvious candidate. But while it is easy to calculate the number knowing the letters, it is not so easy to think of the letters that make that number!

This type of number system was quite common, but each culture used their own alphabet. The Hebrews and the Arabs had a system like this. They also converted words and names into numbers, like the Greeks.

If you are writing a mixture of words and numbers, you will need some way of explaining which is which. The Greeks used the ‘keraia’ after the numeral, a small mark rather like a single quote.

#### Modern use of Greek letters for numbers

Modern Greeks still use these types of numbers for formal use, rather as we would use Roman numbers, although they use Arabic numbers for calculation. However, the form of the archaic letters in particular have changed since Classical Greek times. The symbols above are the Classical Greek ones. Unfortunately, in Classical Greece, they only had capital letters. I have used lower case ones above as it is easier to recognise them as Greek letters, which strictly speaking is inaccurate. For more information, see a discussion on the various forms of Greek numerals.

In Mathematics, we use letters of various alphabets to represent numbers as well, but in a completely different way. In Algebra, we use letters to represent unknowns, or variables in a general formula. The point of the Greek system was that their letters were specific numbers. In fact, mathematicians use certain Greek letters to mean specific constants, but these are quite different values than the ones above. or pi is the ratio of a circle’s circumference to its diameter. is the golden ratio.