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, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers, however, Greece uses Arabic numerals.
The Minoan and Mycenaean civilizations' Linear A and Linear B alphabets used a different system, called Aegean numerals, which included specialised symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000.
Attic numerals was another system that came into use perhaps in the 7th century BC. 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, = 1,000, and = 10,000. The numbers 50, 500, 5,000, and 50,000 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, but the symbols varied with the local alphabets: in Boeotia, was 1,000.
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. More thorough modern archaeology has caused the date to be pushed back at least to the 5th century BC, a little before Athens abandoned its pre-Euclidean alphabet in favour of Miletus's in 402 BC, and it may predate that by a century or two. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over: digamma, koppa, and 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 and its use is unattested in Athens until the 2nd century AD. (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 c. AD 50.)
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 to 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 to koppa. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well, from rho to sampi. (The fact that this was not the traditional location of sampi or its possible predecessor san has led classicists to conclude that it was no longer in use even locally by the time the system was created.)
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 well into the Roman period.) In ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars: α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ (600 + 60 + 6). (Numbers larger than 1,000 reused the same letters but included various marks to note the change.) Fractions were indicated as the denominator followed by a keraia (ʹ); γʹ indicated one third, δʹ one fourth and so on. As an exception, special symbol ∠ʹ indicated one half. These fractions were additive (also known as Egyptian fractions); for example δʹ ϛʹ indicated 1⁄4 + 1⁄6 = 5⁄12.
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 (Ϝ) came to be avoided in favour 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 ϛ ( or ).
In modern Greek, a number of other changes have been made. Instead of extending an over bar 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 (´), the tonos (U+0384,΄) and the prime symbol (U+02B9, ʹ), but has its own Unicode character as U+0374. Alexander the Great's father Philip II of Macedon is thus known as Φίλιππος Βʹ in modern Greek. A lower left keraia (Unicode: U+0375, "Greek Lower Numeral Sign") is now standard for distinguishing thousands: 2019 is represented as ͵ΒΙΘʹ (2 × 1,000 + 10 + 9).
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 and phrases a numeric sum that has meaning through being connected to words, names and phrases of similar sum is called isopsephy (gematria).
|6||ξ||Ξʹ||60||χ||Χʹ||600||͵ & ͵
͵ & ͵
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.
Hellenistic astronomers extended alphabetic Greek numerals into a sexagesimal positional numbering system by limiting each position to a maximum value of 50 + 9 and including a special symbol for zero, which was also used alone like today's modern zero, more than as a simple placeholder. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.) — they were not used for the 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 (c. 380) and Theon's daughter Hypatia (died 415).
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/ + 3/. 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 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.
Alpha (uppercase Α, lowercase α; Ancient Greek: ἄλφα, álpha, modern pronunciation álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of 1.
It was derived from the Phoenician and Hebrew letter aleph - an ox or leader.Letters that arose from alpha include the Latin A and the Cyrillic letter А.
In English, the noun "alpha" is used as a synonym for "beginning", or "first" (in a series), reflecting its Greek roots.Armenian numerals
The system of Armenian numerals is a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet.
There was no notation for zero in the old system, and the numeric values for individual letters were added together. The principles behind this system are the same as for the Ancient Greek numerals and Hebrew numerals. In modern Armenia, the familiar Arabic numerals are used. Armenian numerals are used more or less like Roman numerals in modern English, e.g. Գարեգին Բ. means Garegin II and Գ. գլուխ means Chapter III (as a headline).
The final two letters of the Armenian alphabet, "o" (Օ) and "fe" (Ֆ) were added to the Armenian alphabet only after Arabic numerals were already in use, to facilitate transliteration of other languages. Thus, they do not have a numerical value assigned to them.Attic numerals
The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals (from acrophony) because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.
The Attic numerals were a decimal (base 10) system, like the older Egyptian and the later Etruscan, Roman, and 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 were eventually replaced by the classic Greek numerals 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.Beta
Beta (UK: , US: ; uppercase Β, lowercase β, or cursive ϐ; Ancient Greek: βῆτα, romanized: bē̂ta or Greek: βήτα vita) is the second letter of the Greek alphabet. In the system of Greek numerals it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive /b/. In Modern Greek, it represents the voiced labiodental fricative /v/. Letters that arose from beta include the Roman letter ⟨B⟩ and the Cyrillic letters ⟨Б⟩ and ⟨В⟩.Delta (letter)
Delta (uppercase Δ, lowercase δ or 𝛿; Greek: δέλτα délta, [ˈðelta]) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. It was derived from the Phoenician letter dalet 𐤃, Letters that come from delta include Latin D and Cyrillic Д.
A river delta (originally, the Nile River delta) is so named because its shape approximates the triangular uppercase letter delta. Despite a popular legend, this use of the word delta was not coined by Herodotus.Eta
Eta (uppercase Η, lowercase η; Ancient Greek: ἦτα ē̂ta [êːtaː] or Greek: ήτα ita [ˈita]) is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its sound value in the classical Attic dialect of Ancient Greek was a long vowel [ɛː], raised to [i] in hellenistic Greek, a process known as iotacism.
In the ancient Attic number system (Harodianic or acrophonic numbers), the number 100 was represented by "Η", because it was the initial of ΗΕΚΑΤΟΝ, the ancient spelling of ἑκατόν = "one hundred". In the latter system of (Classical) Greek numerals it has a value of 8.
Eta was derived from the Phoenician letter heth . Letters that arose from eta include the Latin H and the Cyrillic letter И.Iota
Iota (; uppercase Ι, lowercase ι; Greek: ιώτα) is the ninth letter of the Greek alphabet. It was derived from the Phoenician letter Yodh. Letters that arose from this letter include the Latin I and J, the Cyrillic І (І, і), Yi (Ї, ї), and Je (Ј, ј), and iotated letters (e.g. Yu (Ю, ю)).
In the system of Greek numerals, iota has a value of 10.Iota represents the sound [i]. In ancient Greek it occurred in both long [iː] and short [i] versions, but this distinction was lost in Koine Greek.Iota participated as the second element in falling diphthongs, with both long and short vowels as the first element. Where the first element was long, the iota was lost in pronunciation at an early date, and was written in polytonic orthography as iota subscript, in other words as a very small ι under the main vowel. Examples include ᾼ ᾳ ῌ ῃ ῼ ῳ. The former diphthongs became digraphs for simple vowels in Koine Greek.The word is used in a common English phrase, "not one iota", meaning "not the slightest amount", in reference to a phrase in the New Testament (Matthew 5:18): "until heaven and earth pass away, not an iota, not a dot, (King James Version: '[not] one jot or one tittle') will pass from the Law until all is accomplished." (Mt 5:18) This refers to iota, the smallest letter, or possibly Yodh, י, the smallest letter in the Hebrew alphabet.
The word 'jot' (or iot) derives from iota.The German, Portuguese and Spanish name for the letter J (Jot / jota) is derived from iota.Kappa
Kappa (uppercase Κ, lowercase κ or cursive ϰ; Greek: κάππα, káppa) is the 10th letter of the Greek alphabet, used to represent the [k] sound in Ancient and Modern Greek. In the system of Greek numerals, Kʹ has a value of 20. It was derived from the Phoenician letter kaph . Letters that arose from kappa include the Roman K and Cyrillic К.
Greek proper names and placenames containing kappa are often written in English with "c" due to the Romans' transliterations into the Latin alphabet: Constantinople, Corinth, Crete. All formal modern romanizations of Greek now use the letter "k", however: Thessaloniki, Kalamata, Nikaia.
The cursive form ϰ is generally a simple font variant of lower-case kappa, but it is encoded separately in Unicode for occasions where it is used as a separate symbol in math and science. In mathematics, the kappa curve is named after this letter; the tangents of this curve were first calculated by Isaac Barrow in the 17th century.Koppa (letter)
Koppa or qoppa (Ϙ, ϙ; as a modern numeral sign: ) is a letter that was used in early forms of the Greek alphabet, derived from Phoenician qoph . It was originally used to denote the /k/ sound, but dropped out of use as an alphabetic character in favor of Kappa (Κ). It has remained in use as a numeral symbol (90) in the system of Greek numerals, although with a modified shape. Koppa is the source of Latin Q, as well as the Cyrillic numeral sign of the same name (Koppa).Lambda
Lambda (uppercase Λ, lowercase λ; Greek: λάμ(β)δα lám(b)da) is the 11th letter of the Greek alphabet, representing the sound /l/. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed . Letters in other alphabets that stemmed from lambda include the Latin L and the Cyrillic letter El (Л, л). The ancient grammarians and dramatists give evidence to the pronunciation as [laːbdaː] (λάβδα) in Classical Greek times. In Modern Greek the name of the letter, Λάμδα, is pronounced [lamða].
In early Greek alphabets, the shape and orientation of lambda varied. Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets), or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the Ionic alphabet, Greek settled on an angle at the top; the Romans put the angle at the lower-left.
The HTML 4 character entity references for the Greek capital and small letter lambda are "Λ" and "λ", respectively.
The Unicode code points for lambda are U+039B and U+03BB.Mu (letter)
Mu (uppercase Μ, lowercase μ; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) or my is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water, which had been simplified by the Phoenicians and named after their word for water, to become 𐤌img (mem). Letters that derive from mu include the Roman M and the Cyrillic М.Nu (letter)
Nu (/njuː/; uppercase Ν lowercase ν; Greek: νι ni [ni]) or ny is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50. It is derived from the ancient Phoenician language nun . Its Latin equivalent is N, though the lowercase resembles the Roman lowercase v ().
The name of the letter is written νῦ in Ancient Greek and traditional Modern Greek polytonic orthography, while in Modern Greek it is written νι [ni].Numerals in Unicode
Numerals (often called numbers in Unicode) are characters or sequences of characters that denote a number. The Hindu-Arabic numeral system (base-10) is used widely in various writing systems throughout the world and all share the same semantics for denoting numbers. However, the graphemes representing the numerals differ widely from one writing system to another. To support these grapheme differences, Unicode includes encodings of these numerals within many of the script blocks. The decimal digits are repeated in 22 separate blocks. In addition to many forms of the Hindu-Arabic numerals, Unicode also includes several less common numerals such as: Aegean numerals, Roman numerals, counting rod numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, and also composite characters containing Arabic numerals such as ½.
Numerals invariably involve composition of glyphs as a limited number of characters are composed to make other numerals. For example, the sequence 9–9–0 in Arabic numerals composes the numeral for nine hundred ninety (990). In Roman numerals, the same number is expressed by the composed numeral Ⅹↀ or ⅩⅯ. Each of these is a distinct numeral for representing the same abstract number. The semantics of the numerals differ in particular in their composition. Hindu-Arabic digits are positional-value compositions, while the Roman numerals are sign-value and they are additive and subtractive depending on their composition.Omicron
Omicron (uppercase Ο, lowercase ο, literally "small o": όμικρον < ὂ μικρόν - ò mikrón, micron meaning 'small' in contrast to omega) is the 15th letter of the Greek alphabet. In the system of Greek numerals it has a value of 70. This letter is derived from the Phoenician letter ayin . In classical Greek, omicron represented the sound [o] in contrast to omega [ɔː] and ου [oː]. In modern Greek, omicron represents the mid back rounded vowel /o̞/ . Letters that arose from omicron include Roman O and Cyrillic O.
The upper-case letter of omicron (O) was originally used in mathematics as a symbol for Big O notation (representing a function's asymptotic growth rate), but has fallen out of favor because omicron is indistinguishable from the Latin letter O and easily confused with the digit zero (0).
Omicron is used to designate the fifteenth star in a constellation group, its ordinal placement a function of both magnitude and position. Such stars include Omicron Andromedae, Omicron Ceti, and Omicron Persei.Phi
Phi (; uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰé͜e]; Modern Greek φι fi [fi]) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek, it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as ⟨ph⟩. During the later part of Classical Antiquity, in Koine Greek (final centuries BC), its pronunciation shifted to that of a voiceless labiodental fricative ([f]).
The romanization of the Modern Greek phoneme is therefore usually ⟨f⟩.
It may be that phi originated as the letter qoppa and initially represented the sound /kʷʰ/ before shifting to Classical Greek [pʰ]. In traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) descends from phi.
As with other Greek letters, lowercase phi is used as a mathematical or scientific symbol. Some uses, such as the golden ratio, require the old-fashioned 'closed' glyph, which is separately encoded as the Unicode character U+03D5 ϕ GREEK PHI SYMBOL.Pi (letter)
Pi (; uppercase Π, lowercase π and ϖ; Greek: πι [pi]) is the sixteenth letter of the Greek alphabet, representing the sound [p]. In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter Pe (). Letters that arose from pi include Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).Rho
Rho (; uppercase Ρ, lowercase ρ or ϱ; Greek: ῥῶ) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings.Upsilon
Upsilon (; or UK: ; uppercase Υ, lowercase υ; Greek: ύψιλον ýpsilon [ˈipsilon]) or ypsilon is the 20th letter of the Greek alphabet. In the system of Greek numerals, Υʹ has a value of 400. It is derived from the Phoenician waw .Xi (letter)
Xi (uppercase Ξ, lowercase ξ; Greek: ξι) is the 14th letter of the Greek alphabet. It is pronounced [ksi] in Modern Greek, and generally or in English. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh .
Xi is not to be confused with the letter chi, which gave its form to the Latin letter X.
|Origin and genealogy|
|Promotion and study|