Φ

Fi in a capital letter Etymologicum Magnum (1499).

Fi (according to the RAE since 2001) or phi (in capital letters Φ, lowercase φ [variant ϕ]; Ancient Greek call φ(ε)ῖ ph(e)î /pʰêː, pʰîː/, in Modern Greek φι fi /fi/) is the twenty-first letter of the Greek alphabet. The Romans, when transliterating this letter into Latin characters, did so with the digraph ph, thus representing the aspirated p sound ([pʰ]) that it had in ancient Greek: for example, in Phidias, philosophia or Pharao (in Spanish: Phidias, philosophy, pharaoh). In Modern Greek it is pronounced simply [f] as φέτα (feta).

In the Greek numeral system it has a value of 500 (Φʹ).

History

Apparently, fi is not directly based on any examples from the Phoenician alphabet like most other Greek letters, but is instead an invention of the Greeks themselves. For this reason, it is placed at the end of the Greek alphabet after the letters of Phoenician origin, which end in tau.

It is possible that phi originated from the letter qoppa and initially represented the sound /kʷʰ/ before switching to Classical Greek [pʰ]. 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 was used in all local Greek alphabets. There were, above all, two basic shapes, one in which the circle was divided into two parts by a vertical line, and another that had the longer vertical line, continuing below the circle or both below and above it.

Epigraphic variants

In archaic epigraphic sources the following variants appear:

Use

A test of the change in the sound of this letter is found in that the Romans took the Greek word "φορε:ς" twice: in a very old way as "amporea" that ended up originating the Spanish term "Ampoule». Later, they took it again but its pronunciation had changed and gave rise to the term “amphora». Note the change in the second syllable of P to F.

The lowercase letter φ is used to symbolize:

• The Function φ of Euler φ(n).
• In both upper and lower case, the golden number or golden proportion, which has many interesting mathematical properties and is behind many of the geometric proportions present in nature and art.
• In statistics, a regular self-regressive model, AR(p).
• In physics and mathematics, the value of an angle (usually the acimutal angle).
• The job function.
• In geography and geodesy it is used to represent the parallel or latitude and its respective value.
• The empty set (although the modern modified symbol ∅ may be preferable).
• In signal processing, the phase of a sinusoidal signal.
• In electricity, the defasing angle of the electric current with respect to the voltage.
• In field engineering, the internal threading angle of a soil.
• It is used by some to represent philosophy.
• In chemistry, to represent the radical fenile, coming from the benzene.
• In Photography to represent the mark of the focal plane.
• In geology, phi units are used to characterize the grain size of a rock sample. These units are defined as the negative logarithm in base 2 of the sample size (in mm).

The capital letter Φ is used to symbolize:

• Magnetic flow.
• In statistics, a seasonal self-regressive model, AR(P).
• In engineering, the diameter of a circular section is solid or tubular.
• In luminotecnia to represent the luminous flux and is measured in Lux.

Unicode

Unicode includes numerous variations of the letter fi for different uses, among the most frequent are:

Character	Official name	Ideal appearance	Your browser	Use
U+03A6	GREEK CAPITAL LETTER PHI	≈ ≈ {displaystyle Phi,!}	≈	For texts in Greek
U+03C6	GREEK SMALL LETTER PHI	or	φ	For texts in Greek
U+03D5	GREEK PHI SYMBOL	φ φ {displaystyle phi,!}	φ (φ)	For mathematical or technical texts.
U+0278	LATIN SMALL LETTER PHI			To symbolize the deaf bilabial fricative in the International Phontic Alphabet

• Greek, Coptic and Latin

• Other