|WikiProject Greece||(Rated Start-class, High-importance)|
|WikiProject Mathematics||(Rated Start-class, Low-importance)|
- 1 Attic numerals
- 2 "extended by using obsolete letters"
- 3 numeral vs number
- 4 modern Greek
- 5 Ambiguation?
- 6 Limitation of large numbers
- 7 Alternate name ref
- 8 Capital letters
- 9 Zero and seventy
- 10 Spam watch
- 11 These are known as byzantine
- 12 Upper-case / Lower-case
- 13 some letters in TeX
- 14 Largest writable value?
- 15 WP:ERA
- 16 M
- 17 Symbols do not display
- 18 Isopsephy (Gematria)
- 19 Ptolemy
I'm using a Unicode (utf8) MSIE browser and not all of the characters are displaying correctly. Does someone know what the symbols are and can they correct them to work with standard characters? comment by Special:Contributions/184.108.40.206, 21:22, 17 April 2006
- The Attic numerals for 5, 50, 500, 5000, 50000 are not rendered correctly. I think images should be used until wider support for these characters is available. These images could eitehr replace the characters inline, or be a separate summary image of all the numerals.
- —DIV (220.127.116.11 (talk) 00:37, 6 February 2009 (UTC))
"extended by using obsolete letters"
From the article: This requires 27 letters, so the 24-letter Greek alphabet was extended by using three obsolete letters: digamma (ϝ, also used are stigma ϛ or στ) for 6, qoppa (ϟ) for 90, and sampi (ϡ) for 900. See Numerals: Stigma, Koppa, Sampi.
- The three characters were already obsolete in classical Greek as letters or were used only in restricted dialects or locations during classical times. See the reference cited in the article Numerals: Stigma, Koppa, Sampi and Greek alphabet#Obsolete letters. — Joe Kress 04:15, 15 May 2006 (UTC)
numeral vs number
A number is an abstract entity that represents a count or measurement, whereas a numeral is a symbol or group of symbols that represents a number. Therefore, "numeral" is the correct title for this article. Andreas (T) 01:52, 18 May 2006 (UTC)
The line "In modern Greek, upper case is preferred" is the first I knew this is still used. How widespread is it? Is it like Roman numerals in latin-alphabet countires, just a veneer of antiquity not used for serious maths or arithmetic? jnestorius(talk) 22:46, 26 October 2006 (UTC)
- The Greek numerals are used in modern Greek texts approximately to the same extent and in the same context as Roman numerals are used in texts written with the Latin alphabet. For example, they are used exclusively for royalties, for chapters in books, etc. The use of Lower-case letters, however, is very rare. Roman numerals are rarely used.
Examples from the Greek WP and Wikisource:
- They are used generally as ordinal numbers. Names of kings, chapters in a book, but also for instance school classses. Thus, first grade would be Α' τάξη. Roman numerals are very rarely used in Greek, mostly in an academic context. Greek numerals are deffinitely not used for computations, excepting numerology, which seems to be a trend in Greek mystico-nationalistic circles. Note however that your average Greek would only easily recognise Greek numerals up to 6 (the number of grades in primary school), or in the best case 8 (the number of academic semesters). Anything higher than that would require some contemplation to recognise, and anything above 29 would cause much consternation even to your average philologist. Any knowledge of Roman numerals is even more limited, naturally. Another indication that Greek numerals are muchly a dead piece of tradition in Greece is that "Κωνσταντίνος Β'" would be literally pronounced as "Constantine B (the letter)" by most people, rather than "Constantine the Second". That is to say, they fully understand the intended meaning is "the second", but still pronounce the letter alphabetically rather than read it out as a numeral. Druworos 09:28, 28 September 2007 (UTC)
"For example, 2006 is represented as ͵βϛʹ (2000 + 6)." How did they made a difference between e.g. 950 001 and 900 051? Was it both ͵ϡναʹ?18.104.22.168 10:39, 28 September 2007 (UTC) From the example given in the Greek version of this exact article, the answer seems to be that they simply use a space between the numerals. 950,001 would be ͵ϡν αʹ, while 900,051 would be ͵ϡ ναʹ. - Misha 22.214.171.124 (talk) 19:38, 6 December 2008 (UTC)
Limitation of large numbers
I thought Ancient Greek did not have words for higher numbers than tens of thousands. This lead to profound difficulty to imagine large numbers. Archimedes eventually solved the problem by inventing exponentiation. Anyone who can verify this?
2009-03-10 Lena Synnerholm, Märsta, Sweden.
Alternate name ref
- Your ref was from a Wikipedia mirror, Slider.com, which copied it from Wikipedia. The equivalent Wikipedia article is here as it appeared on 15 October 2005 before a merge tag was added in January 2006 and redirected to this article. The alternate name, Ionian numerals, should have been added to this article at that time. I removed your ref because a Wikpedia article cannot be a reference for another Wikipedia article as it is not a reliable source. — Joe Kress (talk) 23:43, 21 June 2009 (UTC)
Zero and seventy
If by Byzantine times zero was written exactly as omicron, and the old notation is still used to this day, how would one distinguish the omicron for 70 from omicron for zero? Wouldn't it be grounds for confusion? 126.96.36.199 (talk) 12:06, 3 November 2009 (UTC)
- The Byzantine zero was only used when copying Hellenistic astronomical works with sexagesimal notation, where the largest allowable number in any sexagesimal position was 59 (νθʹ), thus omicron must mean zero, not seventy. Compare this with our decimal notation, where the largest allowable number is any decimal position is 9. — Joe Kress (talk) 02:40, 11 November 2009 (UTC)
- That was vandalism, not spam. I had to revert further back because the same IP editor added Mars as a link in See also. — Joe Kress (talk) 02:40, 11 November 2009 (UTC)
These are known as byzantine
- Do you have a source for that? I thought they pre-dated the Byzantine era. -- Radagast3 (talk) 21:18, 12 March 2010 (UTC)
Upper-case / Lower-case
Greek minuscule letters weren't invented until the 6th century CE, at the *earlierst*. It seems strange (incorrect) to use them for the whole article on ancient Greek numerals...188.8.131.52 (talk) 22:54, 11 July 2010 (UTC)
The versions of TeX used by Wikipedia now include the archaic letters (stigma) and (koppa):
The precise appearance of these may depend on whether you're using mathJax or not.
I created the table below for use in the article titled Ptolemy's table of chords. It doesn't go beyond 100 because no numbers bigger than 180 are needed there.
Largest writable value?
What is the largest writable value using Greek numerals?
I am not an expert but using the rules as presented here, it appears that:
- ͵θʹ = 9,000
- ͵ϟʹ = 90,000
- ͵ϡʹ = 900,000
Does the "Greek Lower Numeral Sign" (GLNS) stack?
If GLNS stacking is permitted then:
- 9,000,000,000,000,000,000 = ͵͵͵͵͵͵θʹ
GNLS, applied per character or group?
Also, from the syntax described in this article, it is unclear to me if the GLNS applied per letter over 900, or if it is applied to letters in groups of three. Does ͵ϡ͵ϟ͵θʹ or ͵ϡϟθʹ equal 999,000 ?
If GLNS sign stacking is not permitted then it looks like the largest single writable value (without the Myriad) is (assuming the GLNS is used per digit) -- ͵ϡ͵ϟ͵θϡϟθʹ = 999,999 DMahalko (talk) 01:14, 1 March 2012 (UTC)
- There is no indication in the references that the GLNS was used beyond one extra digit - if it was there would be ambiguities and duplications. I propose to make the following change unless counter-evidence can be found:
- To represent numbers from 1,000 to 9,999 the letters α-θ are reused to serve as thousands. A "left keraia" (Unicode U+0375, ‘Greek Lower Numeral Sign’) is put in front of thousands to distinguish them from the standard use. For example, 2011 is represented as ͵βιαʹ (2000 + 11).
- It would then follows that beyond 10,000 the Myriad notation has to be used. As currently phrased there would be no way to indicate whether ͵ριαʹ represents 110,001 or 100,011 (an there would be redundant ways of expressing numbers from 10,000 to 999,999).--Keith Edkins ( Talk ) 19:07, 2 March 2012 (UTC)
The article on sampi is very well done and sourced and clearly states that the Greek letters placed over an M-looking symbol (really a variant san or sampi, not mu) are being multiplied by 1000, not 10 000. Accordingly, I've removed this text from the article:
To represent greater numbers, the Greeks also used the myriad from the old Attic numeral system in their notation. Its value is 10,000; the number of myriads was written above its symbol (M). For example,
Other forms are also possible. When that didn't suffice, the "myriad myriad" (one hundred million, written ΜΜ) was used.
The source here was very good as well (Thomas Little Heath (1931). A Manual of Greek Mathematics. p. 18. ISBN 9780486154442. Retrieved 2 Mar 2011.... in fact, it contains additional information about alternate systems and specifics that should be added to clarify some of the questions above) but I'd really like some direct clarification of when M is 40, 900, 1000×X, or 10000×X rather than just putting everything together with no explanation at all.
Was the myriad M just written larger? Was the Upsilon sometimes included over it important? Was the sampi m (×1000s) only a regional thing or very limited in time? etc... — LlywelynII 09:49, 1 November 2013 (UTC)
Symbols do not display
Although most of the non-Latin characters show properly there are a few, such as in the first sentence of the History Section of the main Article, that appear on my PC as little rectangles. Is this a problem with my setup, or with the way the text has been coded? --DStanB (talk) 15:51, 7 January 2015 (UTC)
Observation reproduced, here is what I see in the first sentence of the History Section:
I added... The art of assigning Greek letters also being thought of as numerals and therefore giving words/names/phrases a numeric sum that has meaning through being connected to words/names/phrases of similar sum is called isopsephy (gematria). - The Decoder 184.108.40.206 (talk) 18:15, 29 May 2015 (UTC)
According to Nobbe's edition, Ptolemy used a different system in his Geography. Apparently, rather than expressing the fractional part as multiples of 1/60, he composited the fractions from increasingly smaller partial fractions, like this: