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Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a
The present system probably developed around
Greek numerals are
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 practice of adding up the number values of Greek letters of words, names and phrases, thus connecting the meaning of words, names and phrases with others with equivalent numeric sums, is called isopsephy. A similar practice adapted for the Hebrew alphabet is referred to as gematria.
- Alternatively, sub-sections of manuscripts are sometimes numbered by lowercase characters (αʹ. βʹ. γʹ. δʹ. εʹ. ϛʹ. ζʹ. ηʹ. θʹ.).
- In Ancient Greek, myriad notation is used for multiples of 10,000, for example for 20,000 or ͵δφξζ (also written on the line as ρκγΜ ͵δφξζ) for 1,234,567.
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.
Pappus of Alexandria reports that Apollonius of Perga developed a simpler system based on powers of the myriad; was 10,000, was 10,0002 = 100,000,000, was 10,0003 = 1012 and so on.
In Ptolemy's table of chords, the first fairly extensive trigonometric table, there were 360 rows, portions of which looked as follows:
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 εὐθειῶν, 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+1⁄2°. In the next column we see π μα γ , meaning 80 + 41/60 + 3/60². That is the length of the chord corresponding to an arc of 84+1⁄2° when the diameter of the circle is 120. The next column, labeled ἐξηκοστῶν, 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.
The Greek sexagesimal placeholder or zero symbol changed over time: The symbol used on 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 the 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 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 οὐδέν meaning "nothing". Note that the letter ο was still used with its original numerical value of 70; however, there was no ambiguity, as 70 could not appear in the fractional part of a sexagesimal 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 and either the center of the Sun (for solar eclipses) or the center of Earth's shadow (for lunar eclipses). All of these zeros took the form ο | ο ο, 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.
|Unicode name||GREEK ZERO SIGN|
|UTF-8||240 144 134 138||F0 90 86 8A|
|UTF-16||55296 56714||D800 DD8A|
|Numeric character reference||𐆊
- Alphabetic numeral system – Type of numeral system
- Attic numerals – Symbolic number notation used by the ancient Greeks
- Cyrillic numerals – Numeral system derived from the Cyrillic script
- Greek mathematics – Mathematics of Ancient Greeks
- Greek numerals in Unicode– Graphemes for various number systems (acrophonic, not alphabetic, numerals)
- Hebrew numerals – Numeral system using letters of the Hebrew alphabet, based on the Greek system
- History of ancient numeral systems – Symbols representing numbers
- History of arithmetic – Aspect of history
- History of communication – Aspect of history
- Isopsephy – Practice of adding up number values of letters in a word to form a single number
- List of numeral system topics
- List of numeral systems
- Number of the beast – Number associated with the Beast of Revelation
- Roman numerals – Numbers in the Roman numeral system
- ^ a b Verdan, Samuel (20 March 2007). "Systèmes numéraux en Grèce ancienne: Description et mise en perspective historique" (in French). Archived from the original on 2 February 2010. Retrieved 2 March 2011.
- ^ ISBN 9780486154442. Retrieved 1 November 2013 – via Google Books.
- ^ Thompson, Edward M. (1893). Handbook of Greek and Latin Palaeography. New York, NY: D. Appleton. p. 114.
- ^ "IG I³ 1387". Searchable Greek Inscriptions. The Packard Humanities Institute. Cornell University & Ohio State University. IG I³ 1387 also known as IG I² 760. Retrieved 1 November 2013.
- ^ Jeffery, Lilian H. (1961). The Local Scripts of Archaic Greece. Oxford, UK: Clarendon Press. pp. 38 ff.
- ^ "Magnesia 4". Searchable Greek Inscriptions. The Packard Humanities Institute. Cornell University & Ohio State University. Magnesia 4 also known as Syll³ 695.b. Retrieved 1 November 2013.
- ^ "IG II² 2776". Searchable Greek Inscriptions. The Packard Humanities Institute. Cornell University & Ohio State University. Retrieved 1 November 2013.
- ^ Edkins, Jo (2006). "Classical Greek Numbers". Archived from the original on 10 May 2013. Retrieved 29 April 2013.
- ^ Heath, Thomas L. A Manual of Greek Mathematics, pp. 14 ff. Oxford Univ. Press (Oxford), 1931. Reprinted Dover (Mineola), 2003. Accessed 1 November 2013.
- ^ Nick Nicholas (9 April 2005). "Numerals: Stigma, Koppa, Sampi". Archived from the original on 5 August 2012. Retrieved 2 March 2011.
- ^ a b Greek number systems - MacTutor
- ^ Mercier, Raymond. "Consideration of the Greek symbol 'zero'" (PDF). — gives numerous examples
Toomer, G.J.Princeton, NJ: Princeton University Press. pp. 306–307.