Pi (letter)

Pi (/ˈpaɪ/; Greek: [pi], uppercase Π, lowercase π) is the sixteenth letter of the Greek alphabet, representing [p]. In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter pe . Letters that arose from pi include Cyrillisexc Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).

Symbol

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

• The product operator in mathematics, indicated with capital pi notation ∏ (in analogy to the use of the capital Sigma Σ as summation symbol).
• In textual criticism, Codex Petropolitanus, a 9th-century, uncial codex of the Gospels, now located in St. Petersburg, Russia.
• In legal shorthand, it represents a plaintiff.
• The osmotic pressure in chemistry. Π=MRT

The lower-case letter π is used as a symbol for:

• The mathematical real transcendental (and thus irrational) constant π ≈ 3.1415926535897932384626433832795028841971…, the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter "π" is the first letter of the Greek words "περιφέρεια" 'periphery' and "περίμετρος" 'perimeter', i.e. the circumference.
• The prime-counting function in mathematics.
• Homotopy groups in algebraic topology.
• Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.
• The hadron called the pi meson or pion.
• Economic profit in microeconomics.
• Inflation rate in macroeconomics.
• A type of chemical bond in which the P-orbitals overlap, called a pi bond.
• The natural projection on the tangent bundle on a manifold.
• The unary operation of projection in relational algebra.
• In reinforcement learning π denotes policy.

History

An early form of pi was , appearing almost like a gamma with a hook.

In the book 'L'alphabet grec', T. H. de Mortain speculates that letter П is a gate, since it is the first letter of "πύλη" (gate of town or temple). Allegedly, the Greeks wanted to represent the shape of the entrance to civilization, such as the gate of the lions in Mycenae. This hypothesis is not shared by any other authority in the field and has no other attestation.

Variant pi

Variant pi or "pomega" ($\varpi\,\!$ or ϖ) is a glyph variant of lower case pi sometimes used in technical contexts as though it were a lower-case omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It is used as a symbol for:

• Angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by $\omega$ but this may be confused with vorticity in a fluid dynamics context).
• Longitude of pericenter, in celestial mechanics.
• Comoving distance in cosmology.
• Single-scattering albedo in Radiative transfer.

The various forms of pi are present in Unicode as:

• U+03A0 Π GREEK CAPITAL LETTER PI (HTML Π<dot-separator> Π)
• U+03C0 π GREEK SMALL LETTER PI (HTML π<dot-separator> π)
• U+03D6 ϖ GREEK PI SYMBOL (HTML ϖ<dot-separator> ϖ)
• U+220F ∏ N-ARY PRODUCT (HTML ∏<dot-separator> ∏)
• U+1D28 ᴨ GREEK LETTER SMALL CAPITAL PI (HTML ᴨ)
• U+1D70B 𝜋 MATHEMATICAL ITALIC SMALL PI (HTML 𝜋)
• U+1D6D1 𝛑 MATHEMATICAL BOLD SMALL PI (HTML 𝛑).

Character Encodings

• Greek / Coptic Pi

Character	Π		π		ϖ		Ⲡ		ⲡ
Unicode name	GREEK CAPITAL LETTER PI		GREEK SMALL LETTER PI		GREEK PI SYMBOL		COPTIC CAPITAL LETTER PI		COPTIC SMALL LETTER PI
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	928	U+03A0	960	U+03C0	982	U+03D6	11424	U+2CA0	11425	U+2CA1
UTF-8	206 160	CE A0	207 128	CF 80	207 150	CF 96	226 178 160	E2 B2 A0	226 178 161	E2 B2 A1
Numeric character reference	Π	Π	π	π	ϖ	ϖ	Ⲡ	Ⲡ	ⲡ	ⲡ
Named character reference	Π		π		ϖ
DOS Greek	143	8F	167	A7
DOS Greek-2	198	C6	234	EA
Windows 1253	208	D0	240	F0
TeX	\Pi		\pi		\varpi

• Mathematical Pi

Character	∏		∐		𝚷		𝛑		𝛱		𝜋
Unicode name	N-ARY PRODUCT		N-ARY COPRODUCT		MATHEMATICAL BOLD CAPITAL PI		MATHEMATICAL BOLD SMALL PI		MATHEMATICAL ITALIC CAPITAL PI		MATHEMATICAL ITALIC SMALL PI
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	8719	U+220F	8720	U+2210	120503	U+1D6B7	120529	U+1D6D1	120561	U+1D6F1	120587	U+1D70B
UTF-8	226 136 143	E2 88 8F	226 136 144	E2 88 90	240 157 154 183	F0 9D 9A B7	240 157 155 145	F0 9D 9B 91	240 157 155 177	F0 9D 9B B1	240 157 156 139	F0 9D 9C 8B
UTF-16	8719	220F	8720	2210	55349 57015	D835 DEB7	55349 57041	D835 DED1	55349 57073	D835 DEF1	55349 57099	D835 DF0B
Numeric character reference	∏	∏	∐	∐	𝚷	𝚷	𝛑	𝛑	𝛱	𝛱	𝜋	𝜋
Named character reference	∏

Character	𝜫		𝝅		𝝥		𝝿		𝞟		𝞹
Unicode name	MATHEMATICAL BOLD ITALIC CAPITAL PI		MATHEMATICAL BOLD ITALIC SMALL PI		MATHEMATICAL SANS-SERIF BOLD CAPITAL PI		MATHEMATICAL SANS-SERIF BOLD SMALL PI		MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PI		MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PI
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120619	U+1D72B	120645	U+1D745	120677	U+1D765	120703	U+1D77F	120735	U+1D79F	120761	U+1D7B9
UTF-8	240 157 156 171	F0 9D 9C AB	240 157 157 133	F0 9D 9D 85	240 157 157 165	F0 9D 9D A5	240 157 157 191	F0 9D 9D BF	240 157 158 159	F0 9D 9E 9F	240 157 158 185	F0 9D 9E B9
UTF-16	55349 57131	D835 DF2B	55349 57157	D835 DF45	55349 57189	D835 DF65	55349 57215	D835 DF7F	55349 57247	D835 DF9F	55349 57273	D835 DFB9
Numeric character reference	𝜫	𝜫	𝝅	𝝅	𝝥	𝝥	𝝿	𝝿	𝞟	𝞟	𝞹	𝞹

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

• П, п - Pe (Cyrillic)
• Р, р - Er (Cyrillic)
• P, p - Pe (Latin)
• Greek letters used in mathematics, science, and engineering#Ππ (pi)