Pi (letter)

Pi /ˈpaɪ/ (uppercase Π, lowercase π and ϖ; Template:Lang-el [pi]) is the sixteenth letter of the Greek alphabet, representing the voiceless bilabial plosive IPA: [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 Latin P, Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).

Uppercase Pi

The uppercase letter Π is used as a symbol for:

• 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.

In science and engineering:

• The product operator in mathematics, indicated with capital pi notation Π (in analogy to the use of the capital Sigma Σ as summation symbol).
• The osmotic pressure in chemistry.
• The viscous stress tensor in continuum mechanics and fluid dynamics.

Lowercase Pi

The lowercase letter π is used as a symbol for:

• The mathematical real transcendental (and thus irrational) constant π ≈ 3.14159..., 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 pion (pi meson).
• 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.
• Policy in reinforcement learning.

The earliest polyamory pride flag design, created by Jim Evans in 1995, in which the lowercase letter π stands for the first letter of polyamory.

• Polyamory (in the earliest polyamory pride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory).

History

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

Variant pi

Variant pi or "pomega" ($\varpi \,\!$ or ϖ) is a glyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercase omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It was also used in the minuscule script. It is 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.
• Mean fitness of a population in biology.
• Fundamental weights of a representation (probably to better distinguish from elements $w$ of the Weyl group, than the usual notation $\omega$).
• The lemniscate constant.

Character encodings

The various forms of pi are present in Unicode as:

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

Character encodings tables

• Greek / Coptic Pi

Character information

Preview	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	dec	hex	dec	hex	dec	hex	dec	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, 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 information

Preview	∏		∐		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	dec	hex	dec	hex	dec	hex	dec	hex	dec	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 information

Preview	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	dec	hex	dec	hex	dec	hex	dec	hex	dec	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

Character information

Preview	ℿ		ℼ
Unicode name	DOUBLE-STRUCK CAPITAL PI		DOUBLE-STRUCK SMALL PI
Encodings	decimal	hex	dec	hex
Unicode	8511	U+213F	8508	U+213C
UTF-8	226 132 191	E2 84 BF	226 132 188	E2 84 BC
Numeric character reference	ℿ	ℿ	ℼ	ℼ

The character encodings in the tables above are intended for use as mathematical symbols. Text written in the Greek language (i.e. words, as opposed to mathematics) should not come from any of the tables on this page, but instead should use the normal Greek letters, which have different code numbers and often a different appearance. Using the mathematical symbols to display words (or vice versa) is likely to result in inconsistent spacing and a clumsy, mismatched appearance.

See also

• П, п – Pe (Cyrillic)
• P, p – Pe (Latin)
• Greek letters used in mathematics, science, and engineering#Ππ (pi)
• Tau