- BBC World News
Thales of Miletus explained the solstice and equinox, predicted eclipses, and invented abstract geometry.
Eudoxus of Cnido, 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.
Hipparchus produced a table of chords, an early trigonometric table.
Euclid wrote a textbook on algebra, number theory, and geometry that is still relevant today.
Aristotle estimated the size of the globe; Pythagoras was the first pure mathematician; And what about Archimedes of Syracuse!
The Hellenes of ancient times left us with a myriad of mathematical achievements, but do you know what numbers they used to do such wonders?
Sticks and something else
One of the number systems that were used in Ancient Greece was the Attic numbering, also known Herodian numerals, as they were described for the first time in a second century manuscript of the great Herodian grammarian.
But they have a third name that indicates what they were like: acrophonic numbers, so called 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 symbol for the number 1,000 because the word for one thousand was Χιλιοι.
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 can still see the vestiges of a more primitive one, which had also been used by the cultures that preceded them – Babylonians, Egyptians and Phoenicians – and which consisted of painting a vertical line for each unit until 9 (here you still see in the signs from 1 to 4).
Basing his first number system on the initials of the names of the numbers was not uncommon as in early civilizations the largest figures were often written in letters so abbreviating them that way was a natural step.
The value of letters
Attic numbering was replaced by the ‘Ionic’ numbers, and by the third century BC they were already used regularly in Greek writing.
The other name by which they are known tells us what they were like: alphabetic numeral systemIn other words, what they did was give values to the letters of the alphabet.
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:
- digamma (Ϝ) or stigma (ϛ) by 6
- qoppa (ϙ) for 90
- until (Ϡ) for 900.
In the image below you can see Greek numbers in a Byzantine manuscript of the hero of Alexandria Metrika.
The first line contains the number “͵θϡϟϛ δʹ ϛʹ” – that is, “9.996 + 1⁄4 + 1⁄6” – in which are all the special numerical symbols: sampi (ϡ), koppa (ϟ) and stigma ( ϛ).
So, each letter represented a number, and the combination of them allowed to represent all the numbers … up to 999, which, you can imagine, was a great inconvenience for such illustrious mathematicians.
More symbols had to be created to overcome the problem.
An apostrophe, at the top or bottom left of the symbols 1 through 9, it converted them into the numbers between 1,000 and 9,000.
With that they came to 9,999.
To go further, they used the symbol to the myriad 10,000 –M– to which they put another one above that indicated by how much it had to be multiplied.
For example: if you wanted to express 20,000, you would write M with a ß (beta = 2) above it.
And when the numbers became very large, they wrote the small number that went to the top before the M, as the astronomer and mathematician Aristarco de Samos did when he wanted to record the figure of 71,755,875:
The numbers were generally written from left to right, although inscriptions from right to left and bustropheedon (that is, one line in one direction and the next in the other) are known.
There was no sign of zero or similar, it was not necessary; the system was additive rather than one based on position or place value.
However, at some point a small group of scientists used a zero as a punctuation mark purely for notational purposes, not as a number. The symbol, when it was not just a blank space, was The for “obol” (a coin of lesser value).
This or the other?
Between 475 a. C. and 325 a. C., Ionic numbers stopped being used in favor of Attic numbering.
But since the end of the 4th century BC. From then on, alphabetic numbers became the preferred system throughout the Greek-speaking world.
They were used until the fall of the Byzantine Empire in the 15th century (and are still used occasionally today).
Remember that you can receive notifications from BBC Mundo. Download the new version of our app and activate them so you don’t miss our best content.
Eddie is an Australian news reporter with over 9 years in the industry and has published on Forbes and tech crunch.