What numbers the ancient Greeks used when they made their amazing discoveries

What numbers the ancient Greeks used when they made their amazing discoveries

Tales de Mileto explained the solstice and the equinox, predicted eclipses and invented abstract geometry.

Cnido eudox, in addition to being the father of mathematical astronomy, devised a theory of proportion, which allowed irrational numbers, a concept of magnitude and a method to find areas and volumes of curvilinear objects.

Hiparco produced a chord table, an early trigonometric table.

Euclid wrote a textbook about algebra, numbers theory and geometry that is still relevant.

Aristotle estimated the size of the globe;Pythagoras was the first pure mathematician;And what about Syracuse Archimedes!

The Hellenos of antiquity left us a myriad of mathematical achievements, but do you know what numbers they used to do such wonders?

Sticks and something else

One of the numerical systems that were used in ancient Greece was the attic numbering, also known Herodian numerals, as they were first described in a manuscript of the second century of the Great Herodian grammarian.

But they have a third name that indicates how they were: acrofonic numbers, called like that because the signs used to represent 5 and the multiples of 10 were taken from the first letters of the name of the numbers.

That is, for example, X was the number 1 symbol.000 Well, the word for a thousand was ??????.

Numbers like 50, 500, 5.000 and 50.000 were formed using multiplicative combinations of the sign for 5 and the other signs.


In this system you still see the vestiges of another more primitive, which had also been used by the cultures that preceded them - Babylonians, Egyptians and Phoenicians - and that consisted of painting a vertical line for each unit until 9 (here you still see itIn the signs from 1 to 4).

Base its first numerical system on the initials of the names of the numbers was not uncommon because in the early civilizations the largest figures used to write with letters so abbreviated them in that way was a natural step.

The value of letters

Attic numbering was replaced by 'Jonic' numbers, and for the third century to.C.They were already used regularly in Greek writing.

The other name with which they are known tells us how they were: system of literacy numerals, that is, what they did was give values to the alphabet letters.


Did you notice that some numbers are missing?

What happens is that the classical Greek alphabet had 24 letters, but they needed 27 symbols, so they took advantage of 3 older letters that have fallen into disuse:

In the following image you can see Greek numbers in a Byzantine manuscript of the hero of Alexandria Metrika.

The first line contains the number "??????"-That's, "9.996 + 1? 4 + 1? 6 "- In which all special numerical symbols are: Sampi (?), Koppa (?) And stigma (?).


Then, each letter represented a number, and the combination of them allowed to represent all the numbers...Until 999, which, you can imagine, was a great inconvenience for such illustrious mathematicians.

More symbols had to be created to overcome the problem.

A apostrophe, at the top or lower to the left of the symbols from 1 to 9 converted them into the numbers between 1.000 and 9.000.

With that they reached 9.999.

To go further, they used the symbol for the Mygic of 10.000 -M- to which they put another above to indicate how much it had to be multiplied.

For example: if you wanted to express 20.000, you wrote M with a ß (beta = 2).


And when the numbers became very large, they wrote the small number that was above before the M, as did the astronomer and mathematician Aristarco of Samos when he wanted to register the figure of 71.755.875:


The numbers were generally written from left to right, although inscriptions are known from right to left and bust (that is, a region in one direction and the next one in the other).

There was no zero or similar sign, because it was not necessary;The system was additive instead of one based on position or positional value.

However, at some point a small group of scientists used a zero as a punctuation sign for purely notation purposes, not as a number.The symbol, when it wasn't simply a blank space, was it?For "Obol" (a lower value coin).

This or the other?

Between 475 to.C.and 325 to.C., Jonic numbers stopped being used in favor of attic numbering.

But since the end of the fourth century to.C.From now on, literacy numbers became the preferred system throughout the Greek speech world.

They were used until the fall of the Byzantine Empire in the fifteenth century (and are still occasionally used today).

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