Phi
Phi (/faɪ/;[1] uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰéî̯]; Modern Greek: φι fi [fi]) is the twenty-first letter of the Greek alphabet.
This article is about the letter of the Greek alphabet. For the irrational number, see Golden ratio. For other uses, see Phi (disambiguation). For similar symbols, see Ø (disambiguation).
In Archaic and Classical Greek (c. 9th to 4th century BC), 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 (c. 4th century BC to 4th century AD), its pronunciation shifted to a voiceless bilabial fricative ([ɸ]), and by the Byzantine Greek period (c. 4th century AD to 15th century AD) it developed its modern pronunciation as 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 (Ϙ, ϙ), and initially represented the sound /kʷʰ/ before shifting to Classical Greek [pʰ].[2] In traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) descends from phi.
Like other Greek letters, lowercase phi (encoded as the Unicode character U+03C6 φ GREEK SMALL LETTER PHI) is used as a mathematical or scientific symbol. Some uses require the old-fashioned 'closed' glyph, which is separately encoded as the Unicode character U+03D5 ϕ GREEK PHI SYMBOL.
The letter phi is commonly used in to represent wave functions in quantum mechanics, such as in the Schrödinger equation and bra–ket notation: .
physics
The 1.618033988749894848204586834... in mathematics,[3] art, and architecture. (Its reciprocal, 1/φ, is and is equal to φ - 1.)
