GREEK NUMERALS, also known as IONIC, IONIAN, MILESIAN, or ALEXANDRIAN
NUMERALS, are a system of writing numbers using the letters of the
Greek alphabet . In modern
Greece
CONTENTS * 1 History * 2 Description * 3 Table * 4 Higher numbers * 5 Zero * 6 See also * 7 References * 8 External links HISTORY The Minoan and Mycenaean civilizations '
Linear A and Linear B
alphabets used a different system, called
Aegean numerals
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 = 1, = 5, = 10, = 100, = 1000,
and = 10000. 50, 500, 5000, and 50000 were represented by the letter
with minuscule powers of ten written in the top right corner: , , ,
and . The same system was used outside of
Attica
The present system probably developed around
Miletus
DESCRIPTION
Greek numerals
Greek numerals
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 (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
Although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive 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 ( and ) and simplified ( and ). The numeral for 6 changed several times. During antiquity, the original letter form of digamma ( ) came to be avoided in favor of a special numerical one ( ). By the Byzantine era , the letter was known as episemon and written as or . This eventually merged with the sigma -tau ligature stigma ( or ). In modern Greek , a number of other changes have been made. Instead
of extending an overbar over an entire number, the KERAIA
(κεραία, lit. "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 (ʹ) similar to
the acute accent (´) but has its own
Unicode
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. 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 ). TABLE ANCIENT BYZANTINE MODERN VALUE ANCIENT BYZANTINE MODERN VALUE ANCIENT BYZANTINE MODERN VALUE ANCIENT BYZANTINE MODERN VALUE α Α΄ 1 ι Ι΄ 10 ρ Ρ΄ 100 " xml:lang="el">͵Α 1000 β Β΄ 2 κ Κ΄ 20 σ Σ΄ 200 ͵β ͵Β 2000 γ Γ΄ 3 λ Λ΄ 30 τ Τ΄ 300 ͵ ͵Γ 3000 δ Δ΄ 4 μ Μ΄ 40 υ Υ΄ 400 ͵ ͵Δ 4000 ε Ε΄ 5 ν Ν΄ 50 φ Φ΄ 500 ͵ε ͵Ε 5000 & " xml:lang="el">Ϛ΄ ΣΤ΄ 6 ξ Ξ΄ 60 χ Χ΄ 600 ͵ & ͵ ͵ " xml:lang="el">͵Ϛ 6000 ζ Ζ΄ 7 ο Ο΄ 70 ψ Ψ΄ 700 ͵ζ ͵Z 7000 η Η΄ 8 π Π΄ 80 ω Ω΄ 800 ͵η ͵H 8000 θ Θ΄ 9 & " xml:lang="el">Ϟ΄ 90 & & & & " xml:lang="el">Ϡ΄ 900 ͵θ ͵Θ 9000 * Alternatively, sub-sections of manuscripts are sometimes numbered {1,2,3,...,9} by lowercase characters {αʹ. βʹ. γʹ. δʹ. εʹ. ϛʹ. ζʹ. ηʹ. θʹ.} * In Ancient Greek, Myriad notation is used for numbers larger than 9,999, e.g. M {displaystyle {stackrel {rho kappa gamma }{mathrm {M} }}} for 1,230,000 or M o o {displaystyle {stackrel {mathrm {sampi} kappa beta gamma tau mathrm {o} beta tau xi eta epsilon upsilon mathrm {o} zeta }{mathrm {M} }}} ͵εωζ´ for extremely large numbers like 9,223,372,036,854,775,807 . HIGHER NUMBERS 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 new numeral scheme with much greater range. ZERO Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus Hellenistic astronomers extended alphabetic
Greek numerals
In Ptolemy\'s table of chords , the first fairly extensive trigonometric table, there were 360 rows, portions of which looked as follows: ' ` o {displaystyle {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 mathrm {o} sigma tau {tilde {omega }}nu \{begin{array}{l}hline pi delta angle '\pi varepsilon \pi varepsilon angle '\hline pi mathrm {stigma} \pi mathrm {stigma} angle '\pi zeta \hline end{array}}&{begin{array}{rrr}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 mathrm {stigma} &vartheta \hline end{array}}&{begin{array}{rrrr}hline circ &circ &mu mathrm {stigma} &kappa varepsilon \circ &circ &mu mathrm {stigma} &iota delta \circ &circ &mu mathrm {stigma} &gamma \hline circ &circ &mu varepsilon &nu beta \circ &circ &mu varepsilon &mu \circ &circ &mu varepsilon width:51.526ex; height:26.176ex;" alt="{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 mathrm {o} sigma tau {tilde {omega }}nu \{begin{array}{l}hline pi delta angle \pi varepsilon \pi varepsilon angle \hline pi mathrm {stigma} \pi mathrm {stigma} angle \pi zeta \hline end{array}}&{begin{array}{rrr}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 mathrm {stigma} &vartheta \hline end{array}}&{begin{array}{rrrr}hline circ &circ &mu mathrm {stigma} &kappa varepsilon \circ &circ &mu mathrm {stigma} &iota delta \circ &circ &mu mathrm {stigma} &gamma \hline circ &circ &mu varepsilon &nu beta \circ &circ &mu varepsilon &mu \circ &circ &mu varepsilon however, there was no ambiguity, as 70 could not appear in the fractional part of a number, and zero was usually omitted when it was the integer. 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
SEE ALSO *
Attic numerals
*
Gematria
*
Greek numerals
REFERENCES * ^ A B Samuel Verdan (20 Mar 2007). "Systèmes numéraux en Grèce
ancienne: description et mise en perspective historique" (in French).
Retrieved 2 Mar 2011.
* ^ A B C Heath, Thomas L. A Manual of Greek Mathematics, pp. 14
ff. Oxford Univ. Press (Oxford), 1931. Reprinted Dover (Mineola ),
2003. Accessed 1 November 2013.
* ^ Thompson, Edward M. Handbook of Greek and Latin Palaeography,
p. 114. D. Appleton (New York), 1893.
* ^ The Packard Humanities Institute (Cornell & Ohio State
Universities). Searchable Greek Inscriptions: "IG I³ 1387" . Accessed
1 November 2013.
* ^ Jeffery, Lilian H. The Local Scripts of Archaic Greece, pp. 38
ff. Clarendon (Oxford), 1961.
* ^ The Packard Humanities Institute (Cornell & Ohio State
Universities). Searchable Greek Inscriptions: "Magnesia 4" . Accessed
1 November 2013.
* ^ The Packard Humanities Institute (Cornell & Ohio State
Universities). Searchable Greek Inscriptions: "IG II² 2776". Accessed
1 November 2013.
* ^ Edkins, Jo (2006). "Classical Greek Numbers". Retrieved 29 Apr
2013.
* ^ Nick Nicholas (9 Apr 2005). "Numerals: Stigma, Koppa, Sampi".
Archived from the original on 2012-08-05. Retrieved 2 Mar 2011.
* ^ Greek number systems - MacTutor
* ^ Neugebauer, Otto (1969) . The Exact Sciences in Antiquity (2
ed.).
Dover Publications . pp. 13–14, plate 2. ISBN
978-0-486-22332-2 .
* ^ Raymond Mercier, "Consideration of the Greek symbol \'zero\'"
(PDF). (1.32 MiB ) Numerous examples
* ^ Ptolemy's
Almagest
EXTERNAL LINKS Wikimedia Commons has media related to GREEK NUMERALS . * The Greek Number Converter * v * t * e ORIGIN AND GENEALOGY * Proto-Greek * Pre-Greek substrate |