View source for Attic numerals

{{short description|Symbolic number notation used by the ancient Greeks}}
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[[File:EPMA-IGI-3-259-272-Tribute-list-3-crop1-cbadj.png|thumb|Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "𐅂" instead of the generic unit sign "Ι". Some amounts are "𐅄" = 50, "ΗΗΗ" = 300, "𐅅ΗΗΗ" = 800, "ΔΔΔ𐅂𐅂𐅂" = 33, "Χ" = 1000, and "Χ𐅅𐅄Δ𐅂𐅂"? = 1562?.]]
[[File:Aegina Prison Attic Numerals.jpg|thumb|Plaque above the main entrance to the orphanage, which later became a prison, on the Greek island of Aegina. The ancient Greek inscription translates as “The Governor erected this orphanage in the year 1828”. The year is shown as Χ𐅅ΗΗΗΔΔΠΙΙΙ.]]
The '''Attic [[numerical digit|numeral]]s''' are a [[number system|symbolic number notation]] used by the [[Ancient Greece|ancient Greeks]].  They were also known as '''Herodianic numerals''' because they were first described in a 2nd-century manuscript by [[Aelius Herodianus|Herodian]]; or as '''acrophonic numerals''' (from [[acrophony]]) because the basic symbols derive from the first letters of the [[Ancient Greek language|(ancient) Greek]] words that the symbols represented. 

The Attic numerals were a decimal (base 10) system, like the older [[Ancient Egypt|Egyptian]] and the later [[Etruscan numerals|Etruscan]], [[Roman numerals|Roman]], and [[Arabic numerals|Hindu-Arabic]] systems. Namely, the number to be represented was broken down into simple multiples (1 to 9) of [[powers of ten]] — units, tens, hundred, thousands, etc..  Then these parts were written down in sequence, in order of decreasing value. As in the basic Roman system, each part was written down using a combination of two symbols, representing one and five times that power of ten.

Attic numerals were adopted possibly starting in the 7th century BCE and although presently called Attic, they or variations thereof were universally used by the Greeks. No other [[numeral system]] is known to have been used on [[Attica|Attic]] inscriptions [[before the Common Era]].<ref name="Gow"/><ref name="Smith"/> Their replacement by the [[Greek numerals|classic Greek numerals]] started in other parts of the Greek World around the 3rd century BCE. They are believed to have served as model for the Etruscan number system, although the two were nearly contemporary and the symbols are not obviously related. {{cn|date=April 2019}}

==The system==

===Symbols===
The Attic numerals used the following main symbols, with the given values:<ref name="Gow">{{cite journal|journal=The Journal of Philology|volume=XXII|year=1883|place=Cambridge|title=The Greek numerical alphabet|author-first=James|author-last=Gow|author-link=James Gow (scholar)|url=https://books.google.com/books?id=gZZNAQAAMAAJ&pg=PA278|pages=278–9}}</ref><ref name="Smith">{{cite book|title=History of Mathematics|author-first=David Eugene|author-last=Smith|author-link=David Eugene Smith|chapter=Reading and writing numbers: Greek numerals|pages=49–51|year=1958|volume=2|chapter-url=https://books.google.com/books?id=uTytJGnTf1kC&pg=PA49|publisher=Dover Publications|isbn=9780486204307|place=New York}}</ref>

{|class="wikitable"
|-
! style="background-color:#FFFDB0;" | Value
! style="background-color:#FFFDB0;" | Symbol
! Talents
! Staters
! Notes
! Etruscan
! Roman
|-
| style="background-color:#FFFDB0;text-align:right" | '''1'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | Ι
| style="font-size:150%;text-align:center" | 
|
| [[Tally marks|Tally mark?]]
| style="text-align:center" | 𐌠
| style="text-align:center" | I
|-
| style="background-color:#FFFDB0;text-align:right" | '''5'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | Π
| style="font-size:150%;text-align:center" | 𐅈
| style="font-size:150%;text-align:center" | 𐅏
| Old Greek: '''Π'''ΕΝΤΕ {{IPA|[pɛntɛ]}} Modern: {{Lang|el|πέντε}}
| style="text-align:center" | 𐌡
| style="text-align:center" | V
|-
| style="background-color:#FFFDB0;text-align:right" | '''10'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | Δ
| style="font-size:150%;text-align:center" | 𐅉
| style="font-size:150%;text-align:center" | 𐅐
| Old Greek: '''Δ'''ΕΚΑ {{IPA|[deka]}} Modern: {{Lang|el|δέκα}}
| style="text-align:center" | 𐌢
| style="text-align:center" | X
|-
| style="background-color:#FFFDB0;text-align:right" | '''50'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | 𐅄
| style="font-size:150%;text-align:center" | 𐅊
| style="font-size:150%;text-align:center" | 𐅑
| "Δ" in "Π": 10 × 5 = 50
| style="text-align:center" | 𐌣
| style="text-align:center" | L
|-
| style="background-color:#FFFDB0;text-align:right" | '''100'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | Η
| style="font-size:150%;text-align:center" | 𐅋
| style="font-size:150%;text-align:center" | 𐅒
| Old Greek: '''Η'''ΕΚΑΤΟΝ {{IPA|[hɛkaton]}} Modern: {{Lang|el|εκατό}}
| style="text-align:center" | 𐌟
| style="text-align:center" | C
|-
| style="background-color:#FFFDB0;text-align:right" | '''500'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | 𐅅
| style="font-size:150%;text-align:center" | 𐅌
| style="font-size:150%;text-align:center" | 𐅓
| "Η" in "Π": 100 × 5 = 500
| style="text-align:center" | ?
| style="text-align:center" | D
|-
| style="background-color:#FFFDB0;text-align:right" | '''1000'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | Χ
| style="font-size:150%;text-align:center" | 𐅍
| style="font-size:150%;text-align:center" | 𐅔
| Old Greek: '''Χ'''ΙΛΙΟΙ {{IPA|[kʰilioi]}} Modern: {{Lang|el|χίλιοι}}
| style="text-align:center" | ?
| style="text-align:center" | M
|-
| style="background-color:#FFFDB0;text-align:right" | '''5000'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | 𐅆
| style="font-size:150%;text-align:center" | 𐅎
| style="font-size:150%;text-align:center" | 
| "Χ" in "Π": 1000 × 5 = 5000
| style="text-align:center" | ?
| style="text-align:center" | <span style="text-decoration:overline;">V</span>
|-
| style="background-color:#FFFDB0;text-align:right" | '''10000'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | Μ
| style="font-size:150%;text-align:center" | 
| style="font-size:150%;text-align:center" | 𐅕
| Old Greek: '''Μ'''ΥΡΙΟΙ {{IPA|[myrioi]}} Modern: {{Lang|el|μύριοι}}
| style="text-align:center" | ?
| style="text-align:center" | <span style="text-decoration:overline;">X</span>
|-
| style="background-color:#FFFDB0;text-align:right" | '''50000'''
| style="background-color:#FFFDB0;font-size:150%;text-align:center" | 𐅇
| style="font-size:150%;text-align:center" | 
| style="font-size:150%;text-align:center" | 𐅖
| "Μ" in "Π": 10000 × 5 = 50000
| style="text-align:center" | ?
| style="text-align:center" | <span style="text-decoration:overline;">L</span>
|}

The symbols representing 50, 500, 5000, and 50000 were composites of an old form of the capital letter [[Pi (letter)|pi]] (with a short right leg) and a tiny version of the applicable power of ten. For example, 𐅆 was five times one thousand.  

====Special symbols====
The fractions "one half" and "one quarter" were written "𐅁" and "𐅀", respectively.

The symbols were slightly modified when used to encode amounts in [[talent (measurement)|talents]] (with a small capital [[tau]], "Τ") or in [[stater]]s (with a small capital [[sigma]], "Σ"). Specific numeral symbols were used to represent one [[Ancient drachma|drachma]] ("𐅂") and ten [[mina (unit)|minas]] "𐅗". 

==== The symbol for 100 ====
The use of "Η" (capital [[eta]]) for 100 reflects the early date of this numbering system.  In the Greek language of the time, the word for a hundred would be pronounced {{IPA|[hɛkaton]}} (with a "rough aspirated" sound /h/) and written "ΗΕΚΑΤΟΝ", because "Η" represented the sound /h/ in the Attic alphabet. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked.<ref>{{cite book|author-first=Arthur Geoffrey|author-last=Woodhead|year=1981|title=The Study of Greek Inscriptions|edition=Second|place=Cambridge|publisher=Cambridge University Press|page=18|isbn=0-521-23188-4}}</ref><ref>{{cite book|author1-last=Smyth|author1-first=Herbert Weir|author1-link=Herbert Weir Smyth|author2-last=Messing|author2-first=Gordon M.|year=2002|orig-year=1920|title=Greek Grammar|edition=Revised|place=Cambridge, MA|publisher=Harvard University Press|page=10|chapter=§14|isbn=0-674-36250-0}}</ref> It was not until [[Aristophanes of Byzantium]] introduced the various accent markings during the Hellenistic period that the [[spiritus asper]] began to represent /h/, resulting in the spelling {{lang|grc|ἑκατόν}}.<ref>As found in [[Katharevousa]], [[polytonic]] Greek in general and Modern Greek in particular before the 1982 [[Greek_diacritics#Official adoption of monotonic system|official adoption of the monotonic system]]; however, neither the /h/ phoneme nor the spiritus asper, or "rough breathing mark", are present in monotonic [[Standard Modern Greek]], resulting in the standard modern spelling {{lang|grc|εκατό}}.</ref>

===Simple multiples of powers of ten===
Multiples 1 to 9 of each power of ten were written by combining the two corresponding "1" and "5" digits, namely:

{|class="wikitable" style="text-align:right;"
| rowspan=2 style="width:10em" | Units   
| Ι || II || III || IIII || Π || ΠI || ΠII || ΠIII || ΠIIII 
|-  
| style="width:3em" | 1
| style="width:3em" | 2
| style="width:3em" | 3
| style="width:3em" | 4
| style="width:3em" | 5
| style="width:3em" | 6
| style="width:3em" | 7
| style="width:3em" | 8
| style="width:3em" | 9
|-
| colspan=10 style="height:2px;background-color:#DDE0FF;" | 
|-
| rowspan=2 |Tens               
| Δ  || ΔΔ || ΔΔΔ || ΔΔΔΔ || 𐅄 || 𐅄Δ || 𐅄ΔΔ || 𐅄ΔΔΔ || 𐅄ΔΔΔΔ 
|-
| 10 || 20 || 30  || 40  || 50 || 60 || 70  || 80  || 90
|-
| colspan=10 style="height:2px;background-color:#DDE0FF;" | 
|-
| rowspan=2 |Hundreds
| Η || ΗΗ || ΗΗΗ || ΗΗΗΗ || 𐅅 || 𐅅Η || 𐅅ΗΗ || 𐅅ΗΗΗ || 𐅅ΗΗΗΗ
|-
| 100 || 200 || 300 || 400 || 500 || 600 || 700 || 800 || 900
|-
| colspan=10 style="height:2px;background-color:#DDE0FF;" | 
|-
| rowspan=2 |Thousands
| Χ || ΧΧ || ΧΧΧ || ΧΧΧΧ || 𐅆 || 𐅆Χ || 𐅆ΧΧ || 𐅆ΧΧΧ || 𐅆ΧΧΧΧ 
|-
| 1000 || 2000 || 3000 || 4000 || 5000 || 6000 || 7000 || 8000 || 9000
|-
| colspan=10 style="height:2px;background-color:#DDE0FF;" | 
|-
| rowspan=2 |Tens of thousands
| Μ || ΜΜ || ΜΜΜ || ΜΜΜΜ || 𐅇 || 𐅇Μ || 𐅇ΜΜ || 𐅇ΜΜΜ || 𐅇ΜΜΜΜ 
|-
| 10000 || 20000 || 30000 || 40000 ||50000 ||60000 ||70000 || 80000|| 90000
|}

Unlike the more familiar Roman numeral system, the Attic system used only the so-called "additive" notation. Thus, the numbers 4 and 9 were written '''ΙΙΙΙ''' and  '''ΠΙΙΙΙ''', not '''ΙΠ''' and '''ΙΔ'''.

===General numbers===
In general, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc..  Then these parts would be written down in sequence, from largest to smallest value. For example:

* 49 =  40 + 9 = ΔΔΔΔ + ΠΙΙΙΙ = '''ΔΔΔΔΠΙΙΙΙ'''
* 2001 = 2000 + 1 = ΧΧ + I = '''ΧΧΙ'''
* 1982 = 1000 + 900 + 80 + 2 = Χ + 𐅅ΗΗΗΗ + 𐅄ΔΔΔ + ΙΙ = '''Χ𐅅ΗΗΗΗ𐅄ΔΔΔΙΙ'''
* 62708 = 60000 + 2000 + 700 + 8 = 𐅇Μ + ΧΧ + 𐅅ΗΗ + ΠΙΙΙ = '''𐅇ΜΧΧ𐅅ΗΗΠΙΙΙ'''.
<!--
{| class="wikitable" style="text-align:center; margin-left:10px; border: 1px #999 solid;" width=480px;
|+ The acrophonic numerals in comparison to the Roman numeral system.

|-
! height=50px | Ι
! <big>Π</big>
! <big>Δ</big>
! 𐅄
! <big>Η</big>
! 𐅅
! <big>Χ</big>
! 𐅆
! <big>Μ</big>

|-
|rowspan="2"|   1
|rowspan="2"|   5
|rowspan="2"|  10
| <small><span style="line-height:100%"> 5 <br> × <br> 10</span></small>
|rowspan="2"| 100
| <small><span style="line-height:100%"> 5 <br> × <br> 100</span></small>
|rowspan="2"|1000
| <small><span style="line-height:100%"> 5 <br> × <br> 1000</span></small>
|           10000

|-
| 50
| 500
| <small><span style="line-height:100%"> 1000 <br> × <br>  5</span></small>
| <small><span style="line-height:100%"> 1000 <br> × <br> 10</span></small>

|-
! width=10% height=50px | <big>I</big>
! width=10% | <big>V</big>
! width=10% | <big>X</big>
! width=10% | <big>L</big>
! width=10% | <big>C</big>
! width=10% | <big>D</big>
! width=10% | <big>M</big>
! width=10% |<big><span style="text-decoration:overline;">V</span></big>
! width=10% |<big><span style="text-decoration:overline;">X</span></big>

|-
|}-->

==Unicode==
{{main|Ancient Greek Numbers (Unicode block)}}
{{Unicode chart Ancient Greek Numbers}}

{{Table_Numeral Systems}}

==See also==

* {{annotated link|Etruscan numerals}}
* {{annotated link|Greek mathematics}}
* {{annotated link|Greek numerals}}
* {{annotated link|History of ancient numeral systems}}
* {{annotated link|List of numeral system topics}}
* {{annotated link|List of numeral systems}}

==Notes and references==
{{reflist}}

{{list of writing systems}}
{{Ancient Greek mathematics}}

[[Category:Numerals]]
[[Category:Ancient Athens]]
[[Category:Greek mathematics|Numerals]]
[[Category:Society of ancient Greece]]

[[de:Griechische Zahlen]]