    phi (uppercase Î¦, lowercase  or ; , pheÃ®, ; modern , fi, ; english: oxford english dictionary, 3rd ed. "phi, n." oxford university press (oxford), 2005.) is the 21st letter of the greek alphabet. in ancient greek, it represented an aspirated voiceless bilabial plosive (), which was the origin of its usual romanization as "ph". in modern greek, it represents a voiceless labiodental fricative () and is correspondingly romanized as "f". its origin is uncertain but it may be that phi originated as the letter qoppa and initially represented the sound  before shifting to classical greek .brixhe, c. "history of the alphabet", in christidÄs &&nbsp;al.'s a history of ancient greek. 2007. in traditional greek numerals, phi has a value of 500 () or  (). the cyrillic letter ef (Ð¤, Ñ) descends from phi. phi is also used as a symbol for the golden ratio and on other occasions in math and science. this use is separately encoded as the unicode glyph . the modern greek pronunciation of the letter is sometimes encountered in english (as ) when the letter is being used in this sense.see, e.g., the da vinci code and the criminal minds episode, "masterpiece". ==  use as a symbol == the lower-case letter Ï (or often its variant, ) is often used to represent the following: *the golden ratio \tfrac{1 + \sqrt{5}}{2} \approx ... in mathematics, art, and architecture. *euler's totient function Ï(n) in number theory; also called euler's phi function. *the cyclotomic polynomial functions Î¦n(x) of algebra. *in algebra, group or ring homomorphisms * in probability theory,  is the probability density function of the normal distribution. * in probability theory,  is the characteristic function of a random variable x. *an angle, typically the second angle mentioned, after Î¸ (theta). especially: **the argument of a complex number. **the phase of a wave in signal processing. **in spherical coordinates, mathematicians usually 
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