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Phi

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Phi

Phi (uppercase Φ, lowercase or ; Ancient Greek: ϕεῖ, pheî, ; modern Greek: φι, fi, ; English: [1]) is the 21st letter of the Greek alphabet. In Ancient Greek, it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as "ph". In modern Greek, it represents a voiceless labiodental fricative ([f]) 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 /kʷʰ/ before shifting to Classical Greek .[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.

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 ϕ. The modern Greek pronunciation of the letter is sometimes encountered in English (as ) when the letter is being used in this sense.[3]

Contents

  • Use as a symbol 1
  • Computing 2
  • See also 3
  • References 4

Use as a symbol

The lower-case letter φ (or often its variant, ϕ) is often used to represent the following:

The upper-case letter Φ is used as a symbol for:

The diameter symbol in engineering, , is often incorrectly referred to as "phi". This symbol is used to indicate the diameter of a circular section; for example, "⌀14" means the diameter of the circle is 14 units.

Computing

In Unicode, there are multiple forms of the phi letter:

Character Name Correct appearance Your browser Usage
U+03A6 GREEK CAPITAL LETTER PHI \Phi\,\! Φ used in Greek texts
U+03C6 GREEK SMALL LETTER PHI or φ used in Greek texts
U+03D5 GREEK PHI SYMBOL \phi\,\! ϕ used in mathematical and technical contexts[5]
U+0278 LATIN SMALL LETTER PHI ɸ used in IPA to symbolise a voiceless bilabial fricative

In ordinary Greek text, the character U+03C6 φ is used exclusively, although this character has considerable glyphic variation, sometimes represented with a glyph more like the representative glyph shown for U+03C6 (φ, the “loopy” form) and less often with a glyph more like the representative glyph shown for U+03D5 (ϕ, the “straight“ form).

Because Unicode represents a character in an abstract way, the choice between glyphs is purely a matter of font design. While some Greek typefaces, most notably "Porson" typefaces (used widely in editions of classical Greek texts), have a "stroked" glyph in this position (), most other typefaces have "loopy" glyphs. This goes for the "Didot" (or "apla") typefaces employed in most Greek book printing (), as well as for the "Neohellenic" typeface often used for ancient texts ().

It is necessary to have the stroked glyph available for some mathematical uses, and U+03D5 GREEK PHI SYMBOL is designed for this function. Prior to Unicode version 3.0 (1998), the glyph assignments in the Unicode code charts were the reverse, and thus older fonts may still show a loopy form \varphi at U+03D5.[5]

For use as a phonetic symbol in IPA, Unicode has a separate codepoint U+0278, LATIN SMALL LETTER PHI, because in this use only the stroked glyph is considered correct. It typically appears in a form adapted to a Latin typographic environment, with a more upright shape than normal Greek letters and with serifs at the top and bottom.

In HTML/XHTML, the upper- and lower-case phi character entity references are Φ (Φ) and φ (φ), respectively.

In LaTeX, the math symbols are \Phi (\Phi\,\!), \phi (\phi\,\!), and \varphi (\varphi\,\!).

The Unicode standard also includes the following variants of phi and phi-like characters:

Character Name Appearance
U+1D60 MODIFIER LETTER SMALL GREEK PHI
U+1D69 GREEK SUBSCRIPT SMALL LETTER PHI
U+1DB2 MODIFIER LETTER SMALL PHI
U+2CAA COPTIC CAPITAL LETTER FI
U+2CAB COPTIC SMALL LETTER FI
U+2C77 LATIN SMALL LETTER TAILLESS PHI
U+1D6BD MATHEMATICAL BOLD CAPITAL PHI
U+1D6D7 MATHEMATICAL BOLD SMALL PHI
U+1D6DF MATHEMATICAL BOLD PHI SYMBOL
U+1D6F7 MATHEMATICAL ITALIC CAPITAL PHI
U+1D711 MATHEMATICAL ITALIC SMALL PHI
U+1D719 MATHEMATICAL ITALIC PHI SYMBOL
U+1D731 MATHEMATICAL BOLD ITALIC CAPITAL PHI
U+1D74B MATHEMATICAL BOLD ITALIC SMALL PHI
U+1D753 MATHEMATICAL BOLD ITALIC PHI SYMBOL
U+1D76B MATHEMATICAL SANS-SERIF BOLD CAPITAL PHI
U+1D785 MATHEMATICAL SANS-SERIF BOLD SMALL PHI
U+1D78D MATHEMATICAL SANS-SERIF BOLD PHI SYMBOL
U+1D7A5 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PHI
U+1D7BF MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PHI
U+1D7C7 MATHEMATICAL SANS-SERIF BOLD ITALIC PHI SYMBOL

See also

References

  1. ^ Oxford English Dictionary, 3rd ed. "phi, n." Oxford University Press (Oxford), 2005.
  2. ^ Brixhe, C. "History of the Alphabet", in Christidēs & al.'s A History of Ancient Greek. 2007.
  3. ^ See, e.g., The Da Vinci Code and the Criminal Minds episode, "Masterpiece".
  4. ^ Evans, Dylans (1996). An introductory dictionary of Lacanian psychoanalysis. Routledge. p. 145.  
  5. ^ a b "Representative Glyphs for Greek Phi". UTR #25: Unicode support for mathematics ( 
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