Which Greek letter is used in maths to show that the values following it should be summed together?
"sigma form ς never occurs inside a word and is never used as a numeral either. Uppercase forms of stigma as a numeral (Ϛ) are rare in practice; when they occur, they can often be confused with uppercase forms of another numeral symbol, koppa (Ϟϟ), which stands for 90. Stigma is encoded in Unicode as ""Greek letter stigma"" U+03DA (Ϛ) and ""Greek small letter stigma"" U+03DB (ϛ). Stigma (letter) Stigma (ϛ) is a ligature of the Greek letters sigma (Σ) and tau (Τ), which was used in writing Greek between the Middle Ages and the 19th century. It is also"
"Summation In mathematics, summation (denoted with an enlarged capital Greek sigma symbol formula_1) is the addition of a sequence of numbers; the result is their ""sum"" or ""total"". If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called ""addends"", or sometimes ""summands"") may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid). For finite sequences"
"symbol"", formula_1, an enlarged form of the upright capital Greek letter Sigma. This is defined as: where ""i"" represents the index of summation; ""a"" is an indexed variable representing each successive term in the series; ""m"" is the lower bound of summation, and ""n"" is the upper bound of summation. The """"i = m"""" under the summation symbol means that the index ""i"" starts out equal to ""m"". The index, ""i"", is incremented by 1 for each successive term, stopping when ""i"" = ""n"". Here is an example showing the summation of squares: Informal writing sometimes omits the definition of"
"symbol. The symbol is an elongated S, representing the Latin word ""Summa"", meaning ""sum"". When finding areas under curves, integration is often illustrated by dividing the area into infinitely many tall, thin rectangles, whose areas are added. Thus, the integral symbol is an elongated s, for sum. Letters of the alphabet in this time were to be used as symbols of quantity; and although much diversity existed with respect to the choice of letters, there were to be several universally recognized rules in the following history. Here thus in the history of equations the first letters of the alphabet were"
"the 1st and 4th row, the remaining cells are filled with its complementary term ""δ"". Similarly, the empty cells in the 2nd column are filled with ""γ""; in 3rd column ""β""; and 4th column ""α"". Each Greek letter appears only once along the rows, but twice along the columns. As such, the row sums are ""α"" + ""β"" + ""γ"" + ""δ"" while the column sums are either 2 (""α"" + ""δ"") or 2 (""β"" + ""γ""). Likewise for the Latin square, which is obtained by flipping the Greek square along the main diagonal and interchanging the corresponding letters. The"
"Sigma Sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς; ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. When used at the end of a word (when the word is not all caps), the final form (ς) is used, e.g. (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end. The shape and alphabetic position of sigma is derived from Phoenician shin 𐤔 . The name of sigma, according to one hypothesis, may continue that of Phoenician Samekh."
"Isopsephy Isopsephy (; ""isos"" meaning ""equal"" and ""psephos"" meaning ""pebble"") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number. The total number is then used as a metaphorical bridge to other words evaluating the equal number, which satisfies ""isos"" or ""equal"" in the term. The early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, which corresponds to ""psephos"" or ""pebble"" and ""counting"" in the term. Isopsephy is related to gematria—the same practice using the Hebrew alphabet and, later, also the English alphabet—and the ancient"
"geometry and numbers"", was a master in composing isopsephic works. In Greek, each unit (1, 2, ..., 9) was assigned a separate letter, each tens (10, 20, ..., 90) a separate letter, and each hundreds (100, 200, ..., 900) a separate letter. This requires 27 letters, so the 24-letter alphabet was extended by using three obsolete letters: digamma ,(also used are stigma or, in modern Greek, ) for 6, qoppa for 90, and sampi for 900. This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to form the total. For"
"example, 241 is represented as σμα (200 + 40 + 1). Isopsephy Isopsephy (; ""isos"" meaning ""equal"" and ""psephos"" meaning ""pebble"") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number. The total number is then used as a metaphorical bridge to other words evaluating the equal number, which satisfies ""isos"" or ""equal"" in the term. The early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, which corresponds to ""psephos"" or ""pebble"" and ""counting"" in the term. Isopsephy is related to gematria—the same practice using"
"the normal Greek letters, with markup and formatting to indicate text style. Sigma Sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς; ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. When used at the end of a word (when the word is not all caps), the final form (ς) is used, e.g. (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end. The shape and alphabetic position of sigma is derived from Phoenician shin 𐤔 . The name"
"many summation identities involving binomial coefficients (a whole chapter of ""Concrete Mathematics"" is devoted to just the basic techniques). Some of the most basic ones are the following. In the following summations, formula_83 is the number of -permutations of. The following are useful approximations (using theta notation): Summation In mathematics, summation (denoted with an enlarged capital Greek sigma symbol formula_1) is the addition of a sequence of numbers; the result is their ""sum"" or ""total"". If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The"
"is equal to the product of the square's order and the middle term, i.e. ""α"" + ""β"" + ""γ"" = 3 ""β"". Thus, the diagonal sums will be equal if we have ""β""s in the main diagonal and ""α"", ""β"", ""γ"" in the skew diagonal. Similarly, for the Latin square. The resulting Greek and Latin squares and their combination will be as below. Note that the Latin square is just a rotation of the Greek square with the corresponding letters interchanged. Substituting the values of the Greek and Latin letters will give the 3×3 magic square. For the odd squares,"
"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 in contrast to ""omega"" and ""ου"" . In modern Greek, omicron represents the . 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"
"(Λ̸) or 03BB (λ̸). Unicode uses the spelling ""lamda"" in character names, instead of ""lambda"", due to ""preferences expressed by the Greek National Body"". These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style. Lambda Lambda, Λ, λ (uppercase ', lowercase '; ""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"
"of 1000. (""For a full table of the signs and their values, see"" Greek numerals.) These values are traditionally romanized as Roman numerals, so that would be translated as Alexander III of Macedon and transliterated as ""Aléxandros III o Makedṓn"" rather than ""Aléxandros G""' or ""Aléxandros 3"". Greek laws and other official documents of Greece which employ these numerals, however, are to be formally romanized using ""decimal"" Arabic numerals. Ancient Greek text did not mark word division with spaces or interpuncts, instead running the words together (""scripta continua""). In the Hellenistic period, a variety of symbols arose for punctuation or"
"leaving out six—for it is the Episemon and not a letter of the usual Greek alphabet:— 1 + 2 + 3 + 4 + 5 + 7 + 8 = 30 Again, we find the fall of the twelfth Aeon, Sophia, indicated in the alphabet; for Λ, which arithmetically denotes 30, the number of the Aeons, is only the eleventh letter in the alphabet. But it set about to seek another like itself, and so the next letter is M, or ΛΛ. Again, add up the numerical value of all the letters of the alphabet ending with λ and we"
"""summand"" derive from the Latin noun ""summa"" ""the highest, the top"" and associated verb ""summare"". This is appropriate not only because the sum of two positive numbers is greater than either, but because it was common for the ancient Greeks and Romans to add upward, contrary to the modern practice of adding downward, so that a sum was literally higher than the addends. ""Addere"" and ""summare"" date back at least to Boethius, if not to earlier Roman writers such as Vitruvius and Frontinus; Boethius also used several other terms for the addition operation. The later Middle English terms ""adden"" and"
"as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics. note: a symbol for the empty set, formula_23, resembles Φ but is not Φ Greek letters used in mathematics, science, and engineering Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as"
"2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, ... ()). The OEIS was limited to plain ASCII text until 2011, and it still uses a linear form of conventional mathematical notation (such as ""f""(""n"") for functions, ""n"" for running variables, etc.). Greek letters are usually represented by their full names, ""e.g."", mu for μ, phi for φ. Every sequence is identified by the letter A followed by six digits, almost always referred to with leading zeros, ""e.g."", A000315 rather than A315. Individual terms of sequences are separated by commas. Digit groups are not separated by commas,"
"make calculations is illustrated down to modern times by the fact that ""calx"" is ""pebble"" in Latin, which is the ethymology for the word ""calculation"". The board contains the letters M (= 10.000), Ψ (Boetian for 1.000), H (= 100), Δ (= 10) and (=5, or possibly the unit symbol for the Drachma). White pebbles are added next to each letter in order to give the number of each quantity unit. Next to them appear the former symbols used to represent the Greek coins: Obol (Boetian symbol O, 1/6 of a Drachma), half an Obol (С) and a quarter of"
"by the first 2 letters. The final letter in the sequence changes in Greek alphabetical order after 9,000 issued plates. For example, Patras plates are codice_2, where ΑΧ represents the Achaia prefecture of which Patras is the capital. When codice_3 is reached the plates turn to codice_4 and this continues until codice_5 is finished. Only the letters from the intersection between the Latin and Greek alphabets by glyph appearance are used, namely Α, Β, Ε, Ζ, Η, Ι, Κ, Μ, Ν, Ο, Ρ, Τ, Υ, Χ (in Greek alphabetical order). This is because Greece is a contracting party to the"
"is represented as ͵ΒΙΗʹ (). 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). 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"
"Gamma Gamma (uppercase , lowercase ; ""gámma"") is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter represents either a voiced velar fricative or a voiced palatal fricative. In the International Phonetic Alphabet and other modern Latin-alphabet based phonetic notations, it represents the voiced velar fricative. The Greek letter Gamma Γ was derived from the Phoenician letter for the /g/ phoneme ( ""gīml""), and as such is cognate with Hebrew ""gimel"" ג. Based"
"1–9; the next nine, beginning with iota (Ι), stand for the multiples of ten (10, 20, etc. up to 90); and the last nine, beginning with rho (Ρ), stand for the hundreds (100 – 900). For this purpose, the 24 letters of the standard classical Greek alphabet were used with the addition of three archaic or local letters: digamma/""wau"" (Ϝ, , originally denoting the sound ) for ""6"", koppa (Ϙ, originally denoting the sound ) for ""90"", and sampi for ""900"". While digamma and koppa were retained in their original alphabetic positions inherited from Phoenician, the third archaic Phoenician character,"
"Alpha Alpha (uppercase , lowercase ; , ""álpha"", ""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. In Ancient Greek, alpha was pronounced and could be either phonemically long ([aː]) or short ([a]). Where there is ambiguity, long"
"Greek numerals which employed the entire alphabet, including the nonstandard letters digamma, stigma, or sigma-tau (placed between epsilon and zeta), koppa (placed between pi and rho), and sampi (placed after omega). As revised in 2001, ELOT 743 provides for the uncommon characters to be given (in Greek) as $ for stigma, + for koppa, and / for sampi. These symbols are not given lower-case equivalents. When used as numbers, the letters are used in combination with the upper ""keraia"" numeral sign ⟨ʹ⟩ to denote numbers from 1 to 900 and in combination with the lower ""keraia"" ⟨͵⟩ to denote multiples"
"uppercase and lowercase gamma are codice_1 and codice_2. These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style. Gamma Gamma (uppercase , lowercase ; ""gámma"") is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter represents either a voiced velar fricative or a voiced palatal fricative. In the International Phonetic Alphabet and other modern Latin-alphabet based"
"and u. Sometimes font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used. The Bayer designation naming scheme for stars typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet before switching to Latin letters. In mathematical finance, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments. The Greek letter forms used in mathematics are often different from those used in Greek-language text: they are designed to"
"the 6th letter of the modern and classical Greek alphabet, denotes a value of seven (7) when used as a numeral. Examples: Zetta- Zetta is a decimal unit prefix in the metric system denoting a factor of 10 or . The prefix was added as an SI prefix to the International System of Units (SI) in 1991 and has the symbol Z. Zetta is evocative of the Latin numeral , meaning ""seven"". Therefore it was used to denote the seventh power of 1000. A prefix of the same value, ""hepta"", was informally introduced a few years before the promulgation of"
"uses, such as lower case epsilon (ε) for an arbitrarily small positive number, lower case pi (π) for the ratio of the circumference of a circle to its diameter, capital sigma (Σ) for summation, and lower case sigma (σ) for standard deviation. Greek letters are used to denote the brighter stars within each of the eighty-eight constellations. In most constellations, the brightest star is designated Alpha and the next brightest Beta etc. For example, the brightest star in the constellation of Centaurus is known as Alpha Centauri. For historical reasons, the Greek designations of some constellations begin with a lower"
"('house'). In Greek, the name was ""bêta"", pronounced in Ancient Greek. It is spelled βήτα in modern monotonic orthography and pronounced . The letter beta was derived from the Phoenician letter beth . The letter Β had the largest number of highly divergent local forms. Besides the standard form (either rounded or pointed, ), there were forms as varied as (Gortyn), and (Thera), (Argos), (Melos), (Corinth), (Megara, Byzantium), (Cyclades). In the system of Greek numerals, beta has a value of 2. Such use is denoted by a number mark: Β′. Beta is used in finance as a measure of investment"
"example, is the same as A similar notation is applied when it comes to denoting the product of a sequence, which is similar to its summation, but which uses the multiplication operation instead of addition (and gives 1 for an empty sequence instead of 0). The same basic structure is used, with formula_21, an enlarged form of the Greek capital letter Pi, replacing the formula_1. It is possible to sum fewer than 2 numbers: These degenerate cases are usually only used when the summation notation gives a degenerate result in a special case. For example, if formula_25 in the definition"
"Theta Theta (, ; uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; ""thē̂ta"" ; Modern: ""thī́ta"" ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals it has the value 9. In Ancient Greek, θ represented the aspirated voiceless dental plosive , but in Modern Greek it represents the voiceless dental fricative . In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle"