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Sha (Ш ш; italics: Ш ш) is a letter of the Glagolitic and Cyrillic script. It commonly represents the voiceless postalveolar fricative /ʃ/, like the pronunciation of ⟨sh⟩ in "sheep" or the somewhat similar voiceless retroflex fricative /ʂ/ in Russian. More precisely, the sound in Russian denoted by ⟨ш⟩ is commonly transcribed as a palatoalveolar fricative but is actually a voiceless retroflex fricative. It is used in every variation of the Cyrillic alphabet for Slavic and non-Slavic languages.
Contents
In English, Sha is romanized as ⟨sh⟩ or as ⟨š⟩, the latter being the equivalent letter in the Latin alphabets of Czech, Slovak, Slovene, Serbian, Croatian, Latvian and Lithuanian.
History
Sha has its earliest origins in Phoenician Shin and is linked closely to Shin's Greek equivalent: Sigma (Σ, σ, ς). (Note the similar form of the modern Hebrew Shin (ש), which is probably the origin of this letter, deriving from the same Proto-Canaanite source). Sha already possessed its current form in Saints Cyril and Methodius's Glagolitic alphabet. Most Cyrillic letter-forms were derived from the Greek, but as there was no Greek sign for the Sha sound (modern Greek uses simply "Σ/σ/ς" to spell the sh-sound in foreign words and names), Glagolitic Sha was adopted unchanged. There is a possibility that Sha was taken from the Coptic alphabet, which is the same as the Greek alphabet but with a few letters added at the end, including one called "shai" which somewhat resembles both sha and shcha (Щ, щ) in appearance.
Use in mathematics
Ш has the distinction of being the only distinctly Cyrillic letter internationally used in mathematics:
In algebraic geometry, the Tate–Shafarevich group of an Abelian variety A over a field K is denoted Ш(A/K), a notation first suggested by J. W. S. Cassels. (Previously it had been denoted TS.)
In a different mathematical context, some authors allude to the shape of the letter Sha when they use the term Shah function for what is otherwise called a Dirac comb.
The shuffle product is often denoted by ш.