# How did ancient Greeks do mathematics? **URL:** \ **Category:** Factual Questions\ **Created:** [November 4, 1999, 2:31pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592 "1999-11-04T14:31:00Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Timothy\_Campbell](https://avatars.discourse-cdn.com/v4/letter/t/958977/32.png) [@Timothy\_Campbell](https://boards.straightdope.com/u/Timothy_Campbell)\ **Post date:** [November 4, 1999, 2:31pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/1 "1999-11-04T14:31:00Z")
The ancient Greeks did some amazing things with mathematics: calculating pi, making Pythagoras famous, etc. My question is this: **\What kind of numbering system did they use?\** I can’t imagine that they could have calculated pi using Roman Numerals. \(Hmm… III . I IV I V IX II XI V III V …)\ At the same time, I’m pretty sure they didn’t use Arabic numerals. So how did they do it? * * * [Afraid to fly](http://users.aol.com/psoftinfo/info_ff.htm)? Hey, I’ve _been_ there! ---
**Author:** ![Alphagene](https://avatars.discourse-cdn.com/v4/letter/a/8e7dd6/32.png) [@Alphagene](https://boards.straightdope.com/u/Alphagene)\ **Post date:** [November 4, 1999, 2:52pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/2 "1999-11-04T14:52:00Z")
EB: > [@](#): > > …there is only meagre evidence of practical mathematics from the early Greek period (roughly, the 8th through the 4th centuries BC). Inscriptions on stone, for example, reveal use of a numeral system the same in principle as the familiar Roman numerals. This may also be relevant: > [@](#): > > the idea of “oneness” can be represented by the Roman numeral I, **by the Greek letter alpha (the first letter) used as a numeral**, by the Hebrew letter aleph (the first letter) used as a numeral, or by the modern numeral 1, which is Hindu-Arabic in origin. * * * Back off, man. I’m a scientist. ---
**Author:** ![handy](https://avatars.discourse-cdn.com/v4/letter/h/b5a626/32.png) [@handy](https://boards.straightdope.com/u/handy)\ **Post date:** [November 4, 1999, 3:27pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/3 "1999-11-04T15:27:00Z")
Fingers & little stones, drawing in the sand. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 4, 1999, 3:41pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/4 "1999-11-04T15:41:00Z")
From “A History of Mathematics” by Carl B. Boyer: The Attic and Ionian notations have both been found in inscriptions, but the Ionian system prevailed arond the third century BC. (Attic notation seen from 454 to 5 BC) (Ionian notation probaby used from 5th century BC, possibly as early as 8th century BC). The Ionian notation used an older version of the Greek alphabet with three extra letters: vau (aka digamma or stigma), koppa and sampi. One letter was used (in alphabetical order) for 1-9, 10-90, 100-900. e.g. 1 = alpha, 2 = beta, 3 = gamma, …, 10 = iota, …, 100 = pi The three older letters occurred in the following position: 6 = vau, 90 = koppa, 900 = sampi For 1000 to 9000, the first 9 letters were used again, with the letter preceded by a stroke or accent. (In this book, the stroke or accent looks somewhat like a comma.) So for example the number 8888 would be written as ,eta omega pi eta For numbers larger than 10000, you would write the letter M (greek myriad) with an integer symbol above or after it, separated by a dot from the the rest of the number, to indicate that the number next to the M should be multiplied by 10000. e.g. 88888888 would be written as M,eta omega pi eta . eta omega pi eta Yo could apply the same principals for the double myriad, 100000000 Fractions are another topic. * * * J’ai assez vécu pour voir que différence engendre haine. Stendhal ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [November 4, 1999, 3:55pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/5 "1999-11-04T15:55:00Z")
_Timothy Campbell: I can’t imagine that they could have calculated pi using Roman Numerals._ 3.14159265358979 = III.IIVIVIXIIVIVIIIVVIIIIXVIIIX (?) ---
**Author:** ![Timothy\_Campbell](https://avatars.discourse-cdn.com/v4/letter/t/958977/32.png) [@Timothy\_Campbell](https://boards.straightdope.com/u/Timothy_Campbell)\ **Post date:** [November 4, 1999, 4:03pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/6 "1999-11-04T16:03:00Z")
**\Arnold\** : Thanks! That was most informative. To be honest, though, their system doesn’t sound a whole heck of a lot easier than Roman Numerals. **\AWB\** : I’m sorry, but I don’t understand the point of your post. Were you trying to express pi in Roman Numerals? I did that in the original post. ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [November 4, 1999, 4:07pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/7 "1999-11-04T16:07:00Z")
Actually, since the decimal “point” _seems_ to rely on a decimal numeric system, the next question is “How did they represent fractions?” * * * Tom~ ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 5, 1999, 6:58am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/8 "1999-11-05T06:58:00Z")
**Timothy Campbell** says: > [@](#): > > To be honest, though, their system doesn’t sound a whole heck of a lot easier than Roman Numerals. Actually it’s closer to our modern notation than the Roman Numeral system. Notice that with the Myriad prefix you can easily write large numbers without many more characters than in the modern arabic notation. The only thing they didn’t think of is having the position of the digit represent a different multiple of a certain base. **tomndebb** says: > [@](#): > > Actually, since the decimal “point” seems to rely on a decimal numeric system, the next question is “How did they represent fractions?” Firstly, the decimal point may seem a misnomer when used with other bases, but you can use that notation with any base. e.g. base 3: 1/3 = 0.1 base 10: 1/3 = 0.3333333… base 16: 1/3 = 0.5555555… Secondly, you don’t need a decimal point to write fractions. e.g. to write 0.125 I can write 1/8. Originally, the Greeks wrote fractions using a mark similar to a quote mark following the number. so for example 1 / 32 would be gamma betta ’ However, that could also be confused with 3.5 or 3 1/2. Later on they came up with a different system that I will have to look up later. * * * J’ai assez vécu pour voir que différence engendre haine. Stendhal ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 4, 1999, 7:03pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/9 "1999-11-04T19:03:00Z")
P.S. In my original post I made two mistakes. 100 = rho, not 100 = pi 88888888 written as M,eta omega pi eta . ,eta omega pi eta * * * J’ai assez vécu pour voir que différence engendre haine. Stendhal ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 4, 1999, 7:05pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/10 "1999-11-04T19:05:00Z")
%#@%$#% **Another** mistake in my post on fractions! 1 / 32 would be lambda betta ’ However, that could also be confused with 30.5 or 30 1/2. * * * J’ai assez vécu pour voir que différence engendre haine. Stendhal ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [November 4, 1999, 10:41pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/11 "1999-11-04T22:41:00Z")
Hmm; we may have the number of the Beast here! What greek letters correspond to 666? ---
**Author:** ![Sofa\_King](https://avatars.discourse-cdn.com/v4/letter/s/58956e/32.png) [@Sofa\_King](https://boards.straightdope.com/u/Sofa_King)\ **Post date:** [November 5, 1999, 12:11am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/12 "1999-11-05T00:11:00Z")
So pi would be upsilon eta ’ ? ---
**Author:** ![Andy](https://avatars.discourse-cdn.com/v4/letter/a/aeb1de/32.png) [@Andy](https://boards.straightdope.com/u/Andy)\ **Post date:** [November 5, 1999, 1:56am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/13 "1999-11-05T01:56:00Z")
I remember my old supervisor telling me that he’d learnt at school how to carry out multiplication and division of roman numerals. I have no idea how this is/was done. Are there a set of rules or something? ---
**Author:** ![Alphagene](https://avatars.discourse-cdn.com/v4/letter/a/8e7dd6/32.png) [@Alphagene](https://boards.straightdope.com/u/Alphagene)\ **Post date:** [November 5, 1999, 5:13am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/14 "1999-11-05T05:13:00Z")
OK, back to EB. They discuss how the Egyptians multiplied. They had a similar system as the Romans, so I’m guessing it applies here too. Pay attention class! > [@](#): > > …for multiplication they introduced a method of successive doubling. For example, to multiply 28 by 11, one constructs a table of multiples of 28 like the following: > > ``` > 1 28 > 2 56 > 4 112 > 8 224 > 16 448 > > ``` > > … … > > The several entries in the first column that together sum to 11 (i.e., 8, 2, and 1) are checked off. The product is then found by adding up the multiples corresponding to these entries; thus, 224 + 56 + 28 = 308, the desired product. Hope that came out right. * * * Back off, man. I’m a scientist. ---
**Author:** ![John\_W.Kennedy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_w.kennedy/32/1031_2.png) [@John\_W.Kennedy](https://boards.straightdope.com/u/John_W.Kennedy)\ **Post date:** [November 5, 1999, 11:52pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/15 "1999-11-05T23:52:00Z")
For divination purposes, it is not necessary to use the “correct” letters. Indeed, it wouldn’t be possible to get 666, because the letter for “6” is digamma (a.k.a. vau), the ancestor of “F”, which was no longer used in the Greek language (and you won’t find it in modern listings of the Greek alphabet). It is only necessary that the letters add up to the right total. But it _is_ 99% certain that these Greek numerals were where 666 comes from. “Nero Caesar” (spelled in Greek) makes 666. Some ancient manuscripts say 616 instead of 666, and that is produced by “Caesar-God”. In Hebrew, by the way, which uses a system like the Greek, certain numbers are written in odd ways (I don’t have a reference to hand to get the actual numbers, but it would be like calling “31”, “twenty-eleven”) to avoid accidently spelling YHWH, the unspeakable Name of God. * * * John W. Kennedy “Compact is becoming contract; man only earns and pays.” – Charles Williams ---
**Author:** ![Kyberneticist](https://avatars.discourse-cdn.com/v4/letter/k/dc4da7/32.png) [@Kyberneticist](https://boards.straightdope.com/u/Kyberneticist)\ **Post date:** [November 23, 1999, 12:42am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/16 "1999-11-23T00:42:00Z")
Slight correction on that 666 thing can be found here: [http://ftp.iafrica.com/l/ll/lloyd/666.htm](http://ftp.iafrica.com/l/ll/lloyd/666.htm) ---
**Author:** ![Kyberneticist](https://avatars.discourse-cdn.com/v4/letter/k/dc4da7/32.png) [@Kyberneticist](https://boards.straightdope.com/u/Kyberneticist)\ **Post date:** [November 23, 1999, 12:47am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/17 "1999-11-23T00:47:00Z")
The Satanists have a good faq too. 🙂 [http://www.satanic.org.au/library/COS/revelation.html](http://www.satanic.org.au/library/COS/revelation.html) ---
**Author:** ![torq](https://avatars.discourse-cdn.com/v4/letter/t/dfb087/32.png) [@torq](https://boards.straightdope.com/u/torq)\ **Post date:** [November 23, 1999, 12:50am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/18 "1999-11-23T00:50:00Z")
I think the “twenty-eleven” thing was actually fifteen, written as 9-6 instead of 10-5. ---
**Author:** ![TheIncredibleHolg](https://avatars.discourse-cdn.com/v4/letter/t/8797f3/32.png) [@TheIncredibleHolg](https://boards.straightdope.com/u/TheIncredibleHolg)\ **Post date:** [November 23, 1999, 9:19am UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/19 "1999-11-23T09:19:00Z")
I can understand that Hebrew thing, but why do the French say “quatre-vingt” (“four-[times]-twenty”) for 80 and “quatre-vingt-dix” (“four-[times]-twenty-[plus]-ten”) for 90?! ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [November 23, 1999, 12:49pm UTC](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592/20 "1999-11-23T12:49:00Z")
> [@](#): > > I can understand that Hebrew thing, but why do the French say “quatre-vingt” (“four-[times]-twenty”) for 80 and “quatre-vingt-dix” (“four-[times]-twenty-[plus]-ten”) for 90?! This should explain it: > [@](#): > > French still uses remnants of a vigesimal system of counting inherited from its Celtic predecessor, the language of the Gaul. Vigesimal counting in Old French is evidenced by another relic in the name of a Paris hospital built in the 13th century to accommodate 300 blind people, which is still called the Hôpital des Quinze-Vingts, that is, the Hospital of the Fifteen Score.\*\* — Celtic Remnants in French and Danish, _Mathematics from the Birth of Numbers_, Jan Gullberg\*\* * * * “It is lucky for rulers that men do not think.” — Adolf Hitler [Next page](https://boards.straightdope.com/t/how-did-ancient-greeks-do-mathematics/5592.md?page=2)