When did the numbers change?

[John L]

I have noticed that the numbers have changed somewhat from Koine Greek to Modern Greek. Especially numbers like 30, 40 50 60, etc. When did these numbers change? When did triakonta change to trianda?

Also, I was wondering if in Greek, did they ever use symbols like we do in English such as 1,2,3,4,5,6,7, etc? When did they start using Roman numerals?

Thanks!!

[whiteoctave]

there was not, as far as i know, every any introduction of 'abstract' symbols so as to represent numbers, rather letters of the Greek alphabet were used, in either case, with various dashes. the system is quite simple, and letters are assigned in alphabetical order, and in consulting a half decent Greek grammar, the scheme should be laid out. one of the more interesting things about this method is that some letters that dropped out from the letter alphabet where they represented phonemes, still remain strong in numerical representation. i have not seen Roman numerals in greek, though they surely exist, but presumably either in official inscriptions demanded by the Romans or in the late period of their domination by Rome and thereafter.

~D

[Eureka]

i have not seen Roman numerals in greek, though they surely exist, but presumably either in official inscriptions demanded by the Romans or in the late period of their domination by Rome and thereafter.

Roman numerals are silly and unwieldy. Why would any self-respecting Greek use them?

[annis]

Roman numerals are silly and unwieldy. Why would any self-respecting Greek use them?

I remain astonished that Greeks and Romans did arithmetic at all. Neither system is exactly convenient for doing sums.

[Eureka]

I remain astonished that Greeks and Romans did arithmetic at all. Neither system is exactly convenient for doing sums.

I disagree; I think the Greek system is almost as good as Hindu-Arabic numerals (pity about zero).

I have no idea how they did non-integral numbers, though. In fact, some Greeks even toyed with infinitesimals (at least I think so, because Zenon of Elea argued against the practice).

[mingshey]

They must have used some kind of abaccus for the calculation and used the numerals only for records. Or for simple calculations they could have used fingers (and toes). Without bothering with numerals, anyway, they could solve up to quadratic equations with a straight rule(without any scale) and a compass.
If they weren't great at addition and substraction, they were the inventor of the purer form of mathematics.

[John L]

How did they do mathmatics?

[mingshey]

How did they do mathmatics?

It would be helpful to have some time to read the Elements by Euclid to learn about the way they did math without numbers. A number was replaced by a square, or a rectagle, or a line. And the addition, subtraction, multiplication, division, and getting a square root, was done by geometrical operations with a rule and a compass. Solving a quadratic equation consists of these five operations. (They got around the problem of irrational numbers by treating one as a side of a square of integer area.)

[John L]

mingshey,

Thanks for the answer! That sounds like Greek math would be hard to learn. What about today, is it any different?

[mingshey]

mingshey,

Thanks for the answer! That sounds like Greek math would be hard to learn. What about today, is it any different?

When Alexander the Great was young he asked Aristotle, his tutor, if there's an easier way to learn math, Aristotle replied that there was no royal road in geometry(to say math). But later Des Cartes had discovered what could be called a royal road in geometry, to say, algebra. Numbers are abstracted into 'unknowns'. These generalized numbers are greatly easy to handle than geometrical objects.

[John L]

Here is a good link for anyone interested in the Greek matematics.

http://www-gap.dcs.st-and.ac.uk/~histor ... mbers.html

[Eureka]

(They got around the problem of irrational numbers by treating one as a side of a square of integer area.)

Presumably, you mean a square of negative integer area?


Does anyone here have any idea how they reresented non-integers?