Π

Pi in a capital letter Etymologicum Magnum (1499).

Pi (uppercase Π, lowercase π [italics ϖ ]; Ancient Greek call π(ε)ῖ p(e)î /pêː, pîː/, in Modern Greek πι pi /pi/) is the sixteenth letter of the Greek alphabet.

In the Greek numeral system it has a value of 80 (Πʹ).

History

The letter pi evolved from the lyric fenicia pe ().

Pi was used in all epicoric Greek alphabets. In its most common archaic form, the left leg was clearly longer than the right, a shape that served as the origin upon which it evolved into the Latin letter P. However, the length of pi's legs evened out over time and it took its current shape. Otherwise pi showed no less variation than other archaic Greek letters, although in Crete, for example, there was a form that resembled the present-day letter C of the Latin alphabet.

Epigraphic variants

In archaic epigraphic sources the following variants appear:

Use

In Modern Greek, the letter pi represents a voiceless bilabial plosive, [p]. This value is the one it also took in ancient Greek. Some dialects also used it to denote the aspirated sound [pʰ], usually denoted Φ in other dialects; this system is found on Crete and on certain islands in the southern Aegean, notably Santorini, Milos, and Anafi.

Pi is also used in the digraph ⟨μπ⟩ to represent the sound of a voiced bilabial stop consonant /b/, for example μπίρα /ˈbira/ 'beer'. Beta (β) is useless for this use because its modern sound is that of a voiced labio-dental fricative /v/.

In the ancient Greek non-positional numeral system, pi represents eighty; for example ‹ρπʹ› represents the number 180.

Symbolism

Number pi

π π {displaystyle pi } is the relationship between the length of a circumference and its diameter in Euclidean geometry.

The ratio between the length of the perimeter of a circle and its diameter is written with the lowercase letter pi, expressed in mathematics as π = 3.14...

The use of Greek letters was already a tradition in other Latin mathematical works, but since the number pi was a quotient between two numbers, they were used in combination with other letters. The first use of the letter pi to express this number dates from 1706, but its popularization with the current value is due to Leonhard Euler's work Mechanica of 1736.

Lowercase

In addition to the number π, the lowercase letter is also used as a symbol for:

• The number π, fundamental mathematical constant ≈ 3,141592
• The letter piss (π) is used as a symbol of Pedagogy.^{[chuckles]required]}
• In economy, profit, devaluation, inflation.^{[chuckles]required]}
• In Number Theory, the function π(x) is the approximate number of prime numbers less or equal to x(see: Theorem of the prime numbers)
• In particle physics, π⁰, π⁺ and π^- It's three forms of a pion.
• In Chemistry, a type of molecular orbital in the covalent links.
• In chemical coligative properties, π represents the unknown of osmotic pressure.

Uppercase

The capital letter Π is used as a symbol for:

• In mathematics, the producer operator.

Timeline Gallery

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  Pi in the cup of Nestor (sixth centuryVIIIa. C.). Read, among others, at the end of the first line "ποτεριον".

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  Think of an Athenian decree in pre-euclide writing of the centuryVa. C. Read, among others, on the fourth line "[».]ν τ».ς πρυτάνες".

• 

  Pi in the bilingual inscription of Kandahar, one of the edicts of Emperor Ashoka, Afghanistan, centuryIIIa. C.

• 

  Pi on the map of Madaba, an early Byzantine mosaic of the centuryVId. C.

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  Pi in the style of uncial calligraphy in the Codex Basilensis, of the centuryVIIId. C.

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  Pi imitating the archaic shape on the facade of the Zappeion Palace, centuryXIX.

Unicode

Pi appears in various forms within Unicode, such as:

• U+03A0 Русский GREEK CAPITAL LETTER PI
• U+03C0 π GREEK SMALL LETTER PI
• U+03D6 π GREEK PI SYMBOL
• U+220F N-ARY PRODUCT
• U+1D28 GREEK LETTER SMALL CAPITAL PI
• U+1D70B π MATHEMATICAL ITALIC SMALL PI
• U+1D6D1 π MATHEMATICAL BOLD SMALL PI.
• Greek

• Maths