GREEK NUMERALS are a system of writing numbers using the letters of
the
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 '
The present system probably developed around
DESCRIPTION _
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
Although the
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
the acute accent (´) but has its own
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 Αʹ 1 ι Ιʹ 10 ρ Ρʹ 100 ">β Βʹ 2 κ Κʹ 20 σ Σʹ 200 ͵β ͵Β 2000 γ Γʹ 3 λ Λʹ 30 τ Τʹ 300 ͵ ͵Γ 3000 δ Δʹ 4 μ Μʹ 40 υ Υʹ 400 ͵ ͵Δ 4000 ε Εʹ 5 ν Νʹ 50 φ Φʹ 500 ͵ε ͵Ε 5000 & ">ξ Ξʹ 60 χ Χʹ 600 ͵ & ͵ ͵ ">ζ Ζʹ 7 ο Οʹ 70 ψ Ψʹ 700 ͵ζ ͵Z 7000 η Ηʹ 8 π Πʹ 80 ω Ωʹ 800 ͵η ͵H 8000 θ Θʹ 9 & & Ϟʹ 90 & & & & "> M o {displaystyle {stackrel {rho oepsilon }{mathrm {M} }}} ͵εωοεʹ for 1,755,875. HIGHER NUMBERS In his text _
ZERO Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus Hellenistic astronomers extended alphabetic
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
SEE ALSO *
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".
Retrieved 2 Mar 2011.
* ^ Neugebauer, Otto (1969) . _The Exact Sciences in Antiquity_ (2
ed.).
EXTERNAL LINKS _ Wikimedia Commons has media related to GREEK NUMERALS _. * The Greek Number Converter * v * t * e ORIGIN AND GENEALOGY * |