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| {{numeral systems}}
| | βιολογικα σαπουνια «Το Χαμόγελο του Παιδιού» ιδρύθηκε από ένα δεκάχρονο αγόρι, τον Ανδρέα Γιαννόπουλο.&nbsp; Ο Ανδρέας υπήρξε ένα παιδί ευτυχισμένο, ένα παιδί χαμογελαστ..." <br> <br>Τιτλος [http://blog.net.gr/Article.asp?Code=021707&db=BlogContent02 Το Χαμόγελο του παιδιού δεν ξεχνά τον πιτσιρίκο που το ξεκίνησε] <br>θεματική ενότητα [http://blog.net.gr/Category.asp?Code=ΚΟΙΝΩΝΙΑ ΚΟΙΝΩΝΙΑ] <br>Λέξη κλειδί [http://blog.net.gr/tag.asp?Code=παιδιά παιδιά] [http://www.ariston-oliveoil.gr/index.asp?Keyword=0000001818 βιολογικα σαπουνια] <br> <br><br>Ο Ανδρέας υπήρξε ένα [http://el.wikipedia.org/wiki/%CE%A0%CE%B1%CE%B9%CE%B4%CE%AF παιδί] ευτυχισμένο, ένα [http://el.wikipedia.org/wiki/%CE%A0%CE%B1%CE%B9%CE%B4%CE%AF παιδί] χαμογελαστό. Με λόγια ώριμα και ουσιαστικά στις 9 Νοεμβρίου 1995 -πριν από 18 χρόνια- έγραψε το ημερολόγιο του, λίγες ημέρες πριν χάσει τη μάχη για τη ζωή, ξαφνιάζοντας και ταρακουνώντας την ελληνική κοινωνία, ζητώντας την ίδρυση ενός Συλλόγου για τα [http://hellasdata.gr/Tag.php?Code=0000000227.%CF%80%CE%B1%CE%B9%CE%B4%CE%AF.html παιδιά] που έχουν ανάγκη, ανεξαρτήτου χρώ [http://el.wikipedia.org/wiki/%CE%9C%CE%BF%CE%BD%CE%AC%CE%B4%CE%B5%CF%82_%CE%91%CF%80%CE%BF%CE%BA%CE%B1%CF%84%CE%AC%CF%83%CF%84%CE%B1%CF%83%CE%B7%CF%82_%CE%A4%CE%AC%CE%BE%CE%B7%CF%82 ΜΑΤ]ος, θρησκείας και φύλου. <br /> Διαβάστε περισσότερα στο [http://www.gossip-tv.gr/inside-stories/Society/story/286353/18-hronia-meta-to-hamogelo-toy-paidioy-den-xehna-ton-pitsiriko-poy-to-xekinise gossip-tv.gr]<br> <br> <br> <br> <br> <br> <br><br>βιολογικα σαπουνια<br> source: http://www.newsbomb.gr/koinwnia/story/367115/to-hamogelo-toy-paidioy-den-xehna-ton-pitsiriko-poy-to-xekinise<br><br>[http://www.ariston-oliveoil.gr/index.asp?Keyword=0000001818 ariston-oliveoil.gr]… |
| {{hatnote|The numerical signs ʹ and ͵ redirect here. For the accent mark ´, see [[Acute accent]].}}
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| '''Greek numerals''' are a [[numeral system|system of representing numbers]] using the letters of the [[Greek alphabet]]. These alphabetic numerals are also known by names '''Ionic''' or '''[[Ionia]]n numerals''', '''[[Miletus|Milesian]] numerals''', and '''[[Alexandria]]n numerals'''. In modern [[Greece]], they are still used for [[ordinal number (linguistics)|ordinal number]]s and in situations similar to those in which [[Roman numerals]] are still used elsewhere in the West. For ordinary [[cardinal number (linguistics)|cardinal number]]s, however, Greece uses [[Arabic numerals]].
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| ==History==
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| The [[Minoans|Minoan]] and [[Mycenæan civilization]]s' [[Linear A]] and [[Linear B]] alphabets used a different system, called [[Aegean numerals]], which included specialized symbols for numbers: <nowiki>|</nowiki> = 1, – = 10, ◦ = 100, ¤ = 1000, and ☼ = 10000.<ref name=Verdan>{{cite web|url=http://www.dma.ens.fr/culturemath/histoire%20des%20maths/htm/Verdan/Verdan.htm|title=Systèmes numéraux en Grèce ancienne: description et mise en perspective historique|author=Samuel Verdan|date=20 Mar 2007|accessdate=2 Mar 2011}} {{fr icon}}</ref>
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| [[Attic numerals]], which were later adopted as the basis for [[Roman numerals]], were the first alphabetic set. They were [[acrophonic]], derived (after the initial one) from the first letters of the names of the numbers represented. They ran {{GrGl|Zeta archaic}} = 1, {{GrGl|Pi archaic}} = 5, {{GrGl|Delta 04}} = 10, {{GrGl|Eta classical}} = 100, {{GrGl|Chi normal}} = 1000, and {{GrGl|Mu classical}} = 10000. {{nowrap|50, 500, 5000, and 50000}} were represented miniscule powers of ten written in the top right corner inside the letter {{GrGl|Pi archaic}}: [[File:Attic_00050.svg|x16px]], [[File:Attic_00500.svg|x16px]], [[File:Attic_05000.svg|x16px]], and [[File:Attic_50000.svg|x16px]].<ref name=Verdan/> The same system was used outside of [[Attica]], but the symbols varied with the [[Archaic Greek alphabets|local alphabets]]: in [[Bœotia]], {{GrGl|Psi_V-shaped}} was 1000.<ref name=heman>Heath, Thomas L. ''A Manual of Greek Mathematics'', [http://books.google.ca/books?id=_HZNr_mGFzQC&pg=PA14 pp. 14 ff.] Oxford Univ. Press (Oxford), 1931. Reprinted Dover ([[Mineola, New York|Mineola]]), 2003. Accessed 1 November 2013.</ref>
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| The present system probably developed around [[Miletus]] in [[Ionia]]. 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use.<ref>Thompson, Edward M. ''Handbook of Greek and Latin Palaeography'', p. 114. D. Appleton (New York), 1893.</ref> More thorough modern archaeology has caused the date to be pushed back at least to the 5th century BC,<ref>The Packard Humanities Institute (Cornell & Ohio State Universities). ''Searchable Greek Inscriptions'': "[http://epigraphy.packhum.org/inscriptions/oi?ikey=1592&bookid=4®ion=1 IG I³ 1387]" [also known as IG I² 760]. Accessed 1 November 2013.</ref> a little before [[Athens (city-state)|Athens]] abandoned its [[pre-Euclidean alphabet]] in favor of [[Ionic alphabet|Miletus]]'s in 402 BC, and it may predate that by a century or two.<ref>Jeffery, Lilian H. ''The Local Scripts of Archaic Greece'', pp. 38 ff. Clarendon (Oxford), 1961.</ref> The present system uses the 24 letters adopted by [[Eucleides]] as well as three [[Phoenician alphabet|Phoenician]] and Ionic ones that were not carried over: [[digamma (letter)|digamma]], [[koppa (letter)|koppa]], and [[sampi (letter)|sampi]]. The position of those characters within the numbering system imply that the first two were still in use (or at least remembered as letters) while the third was not. The exact dating, particularly for sampi, is problematic since its uncommon value means the first attested representative near Miletus does not appear until the 2nd century BC<ref>The Packard Humanities Institute (Cornell & Ohio State Universities). ''Searchable Greek Inscriptions'': "[http://epigraphy.packhum.org/inscriptions/oi?ikey=260445&bookid=509®ion=8&subregion=27 Magnesia 4]" [also known as Syll³ 695.b]. Accessed 1 November 2013.</ref> and its use is unattested in Athens until the 2nd century AD.<ref>The Packard Humanities Institute (Cornell & Ohio State Universities). ''Searchable Greek Inscriptions'': "[http://epigraphy.packhum.org/inscriptions/oi?ikey=5028&bookid=5®ion=1 IG II² 2776]". Accessed 1 November 2013.</ref> (In general, Athens resisted the use of the new numerals for the longest of any of the Greek states but had fully adopted them by AD {{c.|50}}.<ref name=heman/>)
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| ==Description==
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| [[File:Greek minuscule numerals Cod.Const.Pal.Vet.f96r.svg|thumb|right|Greek numerals in a {{c.|1100}} [[Byzantine Empire|Byzantine]] manuscript of [[Hero of Alexandria]]'s ''Metrika''. The first line contains the number "{{lang|grc|{{overline|͵θϡϟϛ}} δʹ ϛʹ}}", i.e. "{{frac|9996|4|6}}". It features each of the special numeral symbols [[sampi]] (ϡ), [[koppa (letter)|koppa]] (ϟ), and [[stigma (letter)|stigma]] (ϛ) in their [[Greek minuscule|minuscule]] forms.]]
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| Greek numerals are [[decimal]], based on powers of 10. The units from 1 to 9 are assigned to the first nine letters of the old [[Ionic alphabet]] from [[alpha (letter)|alpha]] to [[theta (letter)|theta]]. Instead of reusing these numbers to form multiples of the higher powers of ten, however, each multiple of ten from 10 to 90 was assigned its own separate letter from the next nine letters of the Ionic alphabet from [[iota (letter)|iota]] to [[koppa (letter)|koppa]]. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well, from [[rho (letter)|rho]] to [[sampi (letter)|sampi]].<ref>{{cite web|url=http://gwydir.demon.co.uk/jo/numbers/greek/|title=Classical Greek Numbers|last1=Edkins|first1=Jo|year=2006|accessdate=29 Apr 2013}}</ref> (The fact that this was ''not'' the traditional location of [[sampi (letter)|sampi]] or its possible predecessor [[san (letter)|san]] has led classicists to conclude that it was no longer in use even locally by the time the system was created.)
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| This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example, 241 was represented as {{GrGl|Sigma classical}}{{GrGl|Mu classical}}{{GrGl|Alpha classical}} (200 + 40 + 1). (It was not always the case that the numbers ran from highest to lowest: a 4th-century BC inscription at Athens placed the units to the left of the tens. This practice continued in [[Asia Minor]] well into the [[Roman Greece|Roman period]].<ref name=heman/>) In ancient and medieval manuscripts, these numerals were eventually distinguished from letters using [[overbar]]s: {{overline|α}}, {{overline|β}}, {{overline|γ}}, etc. In medieval manuscripts of the [[Book of Revelation]], the [[number of the Beast]] 666 is written as {{overline|χξϛ}} (600 + 60 + 6). Interestingly enough, the Greek translation of Nero is 666 in this system (Greek of [[nu(letter)|nu]] [[epsilon(letter)|epsilon]] [[rho(letter)|rho]] [[omicron(letter)|omicron]] [[nu(letter)|nu]]. ( Numbers larger than 1,000 reused the same letters but included various marks to note the change.
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| Although the [[Greek alphabet#Letter shapes|Greek alphabet]] began with only [[majuscule]] forms, surviving [[papyrus]] manuscripts from [[Roman Egypt|Egypt]] show that [[uncial]] and [[cursive]] [[Greek minuscule|minuscule]] forms began early. These new letter forms sometimes replaced the former ones, especially in the case of the obscure numerals. The old Q-shaped koppa (Ϙ) began to be broken up ([[File:Greek Koppa cursive 02.svg|x16px]] and [[File:Greek Koppa cursive 03.svg|x16px]]) and simplified ([[File:Greek Koppa cursive 04.svg|x16px]] and [[File:Greek Koppa cursive 05.svg|x16px]]). The numeral for 6 changed several times. During antiquity, the original letter form of digamma ({{GrGl|Digamma oblique}}) came to be avoided in favor of a special numerical one ({{GrGl|Digamma angular}}). By the [[Byzantine Greek|Byzantine era]], the letter was known as [[episemon]] and written as {{GrGl|Digamma cursive 02}} or {{GrGl|Digamma cursive 06}}. This eventually merged with the [[sigma (letter)|sigma]]-[[tau (letter)|tau]] [[Typographic ligature|ligature]] [[stigma (letter)|stigma]] ({{GrGl|Digamma cursive 07}} or {{GrGl|Digamma cursive 04}}).
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| In [[modern Greek]], a number of other changes have been made. Instead of extending an overbar over an entire number, the ''keraia'' ({{lang|el|κεραία}}, <small>lit.</small> "hornlike projection") is marked to its upper right, a development of the short marks formerly used for single numbers and fractions. The modern ''keraia'' is a symbol (<big>ʹ</big>) similar the [[acute accent]] (´) but has its own [[Unicode]] character as U+0374. Exclusive use of [[uppercase letter]]s is also now standard. [[Alexander the Great]]'s father [[Philip II of Macedon]] is thus known as {{lang|el|Φίλιππος Βʹ}} in modern Greek. A lower left ''keraia'' (Unicode: U+0375, "Greek Lower Numeral Sign") is now standard for distinguishing thousands: 2013 is represented as ͵ΒΙΓʹ (2000 + 10 + 3).
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| The declining use of ligatures in the 20th century also means that stigma is frequently written as the separate letters ΣΤʹ, although a single ''keraia'' is used for the group.<ref>{{cite web|url=http://www.tlg.uci.edu/~opoudjis/unicode/numerals.html|title=Numerals: Stigma, Koppa, Sampi|author=Nick Nicholas|date=9 Apr 2005|accessdate=2 Mar 2011}}</ref>
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| ==Table==
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| {{anchor|Chart|List}}
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| {| border="1" cellpadding="5" cellspacing="0"
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| ! |Ancient!!Byzantine!!Modern!!rowspan=2|Value!!rowspan=11| !!Ancient!!Byzantine!!Modern!!rowspan=2|Value!!rowspan=11| !!Ancient!!Byzantine!!Modern!!rowspan=2|Value!!rowspan=11| !!Ancient!!Byzantine!!Modern!!rowspan=2|Value
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| |colspan="3" align="center"|'''Greek'''||colspan="3" align="center"|'''Greek'''||colspan="3" align="center"|'''Greek'''||colspan="3" align="center"|'''Greek'''
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| |{{GrGl|Alpha classical}}||{{overline|α}}||{{lang|el|Αʹ}}||[[1 (number)|1]]||{{GrGl|Iota classical}}||{{overline|ι}}||{{lang|el|Ιʹ}}||[[10 (number)|10]]||{{GrGl|Rho classical}}||{{overline|ρ}}||{{lang|el|Ρʹ}}||[[100 (number)|100]]||{{GrGl|Sampi 1000}} & {{GrGl|Sampi 1000 (2)}}||͵α||{{lang|el|͵Α}}||[[1000 (number)|1000]]
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| |{{GrGl|Beta classical}}||{{overline|β}}||{{lang|el|Βʹ}}||[[2 (number)|2]]||{{GrGl|Kappa classical}}||{{overline|κ}}||{{lang|el|Κʹ}}||[[20 (number)|20]]||{{GrGl|Sigma classical}}||{{overline|σ}}||{{lang|el|Σʹ}}||[[200 (number)|200]]||<sup>[[File:Greek_Beta_classical.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵β||{{lang|el|͵Β}}||[[2000 (number)|2000]]
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| |{{GrGl|Gamma classical}}||{{overline|Γ}}||{{lang|el|Γʹ}}||[[3 (number)|3]]||{{GrGl|Lambda classical}}||{{overline|λ}}||{{lang|el|Λʹ}}||[[30 (number)|30]]||{{GrGl|Tau classical}}||{{overline|τ}}||Τʹ||[[300 (number)|300]]||<sup>[[File:Greek_Gamma_classical.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵{{GrGl|Gamma 02}}||{{lang|el|͵Γ}}||[[3000 (number)|3000]]
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| |{{GrGl|Delta classical}}||{{overline|Δ}}||{{lang|el|Δʹ}}||[[4 (number)|4]]||{{GrGl|Mu classical}}||{{overline|μ}}||{{lang|el|Μʹ}}||[[40 (number)|40]]||{{GrGl|Upsilon classical}}||{{overline|υ}}||{{lang|el|Υʹ}}||[[400 (number)|400]]||<sup>[[File:Greek_Delta_classical.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵{{GrGl|Delta classical}}||{{lang|el|͵Δ}}||[[4000 (number)|4000]]
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| |{{GrGl|Epsilon classical}}||{{overline|ε}}||{{lang|el|Εʹ}}||[[5 (number)|5]]||{{GrGl|Nu classical}}||{{overline|ν}}||{{lang|el|Νʹ}}||[[50 (number)|50]]||{{GrGl|Phi classical}}||{{overline|φ}}||{{lang|el|Φʹ}}||[[500 (number)|500]]||<sup>[[File:Greek_Epsilon_classical.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵ε||{{lang|el|͵Ε}}||[[5000 (number)|5000]]
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| |{{GrGl|Digamma oblique}}<br>{{GrGl|Digamma angular}}||{{GrGl|Digamma cursive 02}} & {{GrGl|Digamma cursive 04}}<br>{{GrGl|Digamma cursive 06}} & {{GrGl|Digamma cursive 07}}||{{lang|el|Ϛʹ}}<br>{{lang|el|ΣΤʹ}}||[[6 (number)|6]]||{{GrGl|Xi classical}}||{{overline|ξ}}||Ξʹ||[[60 (number)|60]]||{{GrGl|Chi classical}}||{{overline|χ}}||{{lang|el|Χʹ}}||[[600 (number)|600]]||<sup>[[File:Greek_Digamma_angular.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵{{GrGl|Digamma cursive 02}} & ͵{{GrGl|Digamma cursive 04}}<br>͵{{GrGl|Digamma cursive 06}} & ͵{{GrGl|Digamma cursive 07}}||{{lang|el|͵Ϛ}}||[[6000 (number)|6000]]
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| |{{GrGl|Zeta classical}}||{{overline|ζ}}||{{lang|el|Ζʹ}}||[[7 (number)|7]]||{{GrGl|Omicron classical}}||{{overline|ο}}||{{lang|el|Οʹ}}||[[70 (number)|70]]||{{GrGl|Psi classical}}||{{overline|ψ}}||{{lang|el|Ψʹ}}||[[700 (number)|700]]||<sup>[[File:Greek_Zeta_classical.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵ζ||{{lang|el|͵Z}}||[[7000 (number)|7000]]
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| |{{GrGl|Eta classical}}||{{overline|η}}||{{lang|el|Ηʹ}}||[[8 (number)|8]]||{{GrGl|Pi classical}}||{{overline|π}}||{{lang|el|Πʹ}}||[[80 (number)|80]]||{{GrGl|Omega classical}}||{{overline|ω}}||{{lang|el|Ωʹ}}||[[800 (number)|800]]||<sup>[[File:Greek_Eta_classical.svg|x8px]]</sup><sub>[[File:Greek_Sampi_palaeographic_02.svg|x16px]]</sub>||͵η||{{lang|el|͵H}}||[[8000 (number)|8000]]
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| |{{GrGl|Theta classical}}||{{overline|θ}}||{{lang|el|Θʹ}}||[[9 (number)|9]]||{{GrGl|Koppa normal}}<br>{{GrGl|Koppa cursive 01}}||{{GrGl|Koppa cursive 02}} & {{GrGl|Koppa cursive 04}}<br>{{GrGl|Koppa cursive 03}} & {{GrGl|Koppa cursive 05}}||{{lang|el|Ϟʹ}}||[[90 (number)|90]]||{{GrGl|Sampi Ionian}}<br>{{GrGl|Sampi palaeographic 05}} & {{GrGl|Sampi palaeographic 15}}<br>{{GrGl|Sampi palaeographic 06}} & {{GrGl|Sampi palaeographic 09}}||{{GrGl|Sampi palaeographic 03}} & {{GrGl|Sampi palaeographic 07}}<br>{{GrGl|Sampi palaeographic 08}}<br>{{GrGl|Sampi palaeographic 10}} & {{GrGl|Sampi palaeographic 11}}<br>{{GrGl|Sampi palaeographic 14}} & {{GrGl|Sampi palaeographic 13}}<br>[[File:Sampi.svg|x16px]]||{{lang|el|Ϡʹ}}||[[900 (number)|900]]||{{GrGl|Sampi 9000}}||͵θ||{{lang|el|͵Θ}}||[[9000 (number)|9000]]
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| |}
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| ==Higher numbers==
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| In his text ''[[The Sand Reckoner]]'', the natural philosopher [[Archimedes]] gives an upper bound of the number of grains of sand required to fill the entire universe, using a contemporary estimation of its size. This would defy the then-held notion that it is impossible to name a number greater than that of the sand on a beach or on the entire world. In order to do that, he had to devise a [[The Sand Reckoner#Naming large numbers|new numeral scheme]] with much greater range.
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| ==Zero==
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| {{anchor|Hellenistic zero}}<!--linked from "Number"-->
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| [[Hellenistic civilization|Hellenistic]] [[astronomer]]s extended alphabetic Greek numerals into a [[sexagesimal]] [[positional notation|positional]] [[numeral system|numbering system]] by limiting each position to a maximum value of 50 + 9 and including a special symbol for [[0 (number)|zero]], which was also used alone like our modern zero, more than as a simple placeholder. However, the positions were usually limited to the fractional part of a number (called [[minute]]s, seconds, thirds, fourths, etc.) — they were not used for the [[integer|integral]] part of a number. This system was probably adapted from [[Babylonian numerals]] by [[Hipparchus]] c. 140 BC. It was then used by [[Ptolemy]] (c. 140), [[Theon of Alexandria|Theon]] (c. 380) and Theon's daughter [[Hypatia of Alexandria|Hypatia]] (murdered 415).
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| In [[Ptolemy's table of chords]], the first fairly extensive trigonometric table, there were 360 rows, portions of which looked as follows:
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| : <math>
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| \begin{array}{ccc} \pi\varepsilon\varrho\iota\varphi\varepsilon\varrho\varepsilon\iota\tilde\omega\nu & \varepsilon\overset{\text{'}}\nu\vartheta\varepsilon\iota\tilde\omega\nu & \overset{\text{`}}\varepsilon\xi\eta\kappa\omicron\sigma\tau\tilde\omega\nu \\
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| \begin{array}{|l|} \hline \pi\delta\angle' \\ \pi\varepsilon \\ \pi\varepsilon\angle' \\ \hline \pi\stigma \\ \pi\stigma\angle' \\ \pi\zeta \\ \hline \end{array} & \begin{array}{|r|r|r|} \hline \pi & \mu\alpha & \gamma \\ \pi\alpha & \delta & \iota\varepsilon \\ \pi\alpha & \kappa\zeta & \kappa\beta \\ \hline \pi\alpha & \nu & \kappa\delta \\ \pi\beta & \iota\gamma & \iota\vartheta \\ \pi\beta & \lambda\stigma & \vartheta \\ \hline \end{array} & \begin{array}{|r|r|r|r|} \hline \circ & \circ & \mu\stigma & \kappa\varepsilon \\ \circ & \circ & \mu\stigma & \iota\delta \\ \circ & \circ & \mu\stigma & \gamma \\ \hline \circ & \circ & \mu\varepsilon & \nu\beta \\ \circ & \circ & \mu\varepsilon & \mu \\ \circ & \circ & \mu\varepsilon & \kappa\vartheta \\ \hline \end{array}
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| \end{array}
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| </math> | |
| Each number in the first column, labeled περιφερειῶν, is the number of degrees of arc on a circle. Each number in the second column, labeled ευθειῶν, is the length of the corresponding chord of the circle, when the diameter is 120. Thus πδ represents an 84° arc, and the ∠' after it means one-half, so that πδ∠' means 84.5°. In the next column we see π μα γ, meaning 80 + 41/60 + 3/60<sup>2</sup>. That is the length of the chord corresponding to an arc of 84.5° when the diameter of the circle is 120. The next column, labeled ὲξηκοστῶν, for "sixtieths", is the number to be added to the chord length for each 1° increase in the arc, over the span of the next 12°. Thus that last column was used for [[linear interpolation]].
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| The Greek sexagesimal placeholder or zero symbol changed over time. The symbol used on [[papyrus|papyri]] during the second century was a very small circle with an overbar several diameters long, terminated or not at both ends in various ways. Later, the overbar shortened to only one diameter, similar to our modern ''o'' macron (ō) which was still being used in late medieval Arabic manuscripts whenever alphabetic numerals were used. But the overbar was omitted in [[Byzantine Empire|Byzantine]] manuscripts, leaving a bare ''ο'' (omicron). This gradual change from an invented symbol to ο does not support the hypothesis that the latter was the initial of ουδέν meaning "nothing".<ref>{{Cite book | edition = 2 | publisher = [[Dover Publications]] | last = Neugebauer | first = Otto | author-link = Otto E. Neugebauer | title = The Exact Sciences in Antiquity | origyear = 1957 | year = 1969 | isbn = 978-0-486-22332-2 | pages = 13–14, plate 2}}</ref><ref>Raymond Mercier, {{PDFlink|[http://www.raymondm.co.uk/prog/GreekZeroSign.pdf Consideration of the Greek symbol 'zero']|1.32 [[Mebibyte|MiB]]<!-- application/pdf, 1384420 bytes -->}} Numerous examples</ref>
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| Some of Ptolemy's true zeros appeared in the first line of each of his eclipse tables, where they were a measure of the angular separation between the center of the [[Moon]] and either the center of the [[Sun]] (for [[solar eclipse]]s) or the center of [[Earth]]'s shadow (for [[lunar eclipse]]s). All of these zeros took the form 0 | 0 0, where Ptolemy actually used three of the symbols described in the previous paragraph. The vertical bar (|) indicates that the integral part on the left was in a separate column labeled in the headings of his tables as ''digits'' (of five arc-minutes each), whereas the fractional part was in the next column labeled ''minute of immersion'', meaning sixtieths (and thirty-six-hundredths) of a digit.<ref>''Ptolemy's [[Almagest]]'', translated by [[G. J. Toomer]], Book VI, (Princeton, NJ: Princeton University Press, 1998), pp. 306–7.</ref>
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| == See also ==
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| *[[Attic numerals]]
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| *[[Gematria]]
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| *[[Unicode_numerals#Ancient_Greek_numerals|Greek numerals in Unicode]] (acrophonic, not alphabetic, numerals)
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| *[[Isopsephy]]
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| ==References==
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| {{Reflist|30em}}
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| ==External links==
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| {{Commons category|Greek numerals}}
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| * [http://www.russellcottrell.com/greek/utilities/GreekNumberConverter.htm The Greek Number Converter]
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| {{Greek language}}
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| {{Ancient Greece topics}}
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| {{DEFAULTSORT:Greek Numerals}}
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| [[Category:Numeral systems]]
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| [[Category:Numerals]]
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| [[Category:Greek mathematics|Numerals]]
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