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Phi (/ f aɪ /; [1] uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî; Modern Greek: φι fi) is the twenty-first letter of the Greek alphabet. In Archaic and Classical Greek (c. 9th to 4th century BC), it represented an aspirated voiceless bilabial plosive ( [pʰ] ), which was the origin of its usual romanization as ph .
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
By 1910, inventor Mark Barr began using the Greek letter phi ( ) as a symbol for the golden ratio. [32] [e] It has also been represented by tau ( ), the first letter of the ancient Greek τομή ('cut' or 'section'). [35] Dan Shechtman demonstrates quasicrystals at the NIST in 1985 using a Zometoy model.
Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts often have specific, fixed meanings in particular areas of mathematics.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. [2] [3] It was derived from the earlier Phoenician alphabet, [4] and is the earliest known alphabetic script to have developed distinct letters for vowels as well as consonants. [5]
This is a list of letters of the Greek alphabet. The definition of a Greek letter for this list is a character encoded in the Unicode standard that a has script property of "Greek" and the general category of "Letter". An overview of the distribution of Greek letters is given in Greek script in Unicode.
It is written using the Greek letter phi as () or (), and may also be called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd( n , k ) is equal to 1.