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The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the fraction part at the right of it. [ 24 ] A radix point is most often used in decimal (base 10) notation, when it is more commonly called the decimal point (the prefix deci- implying base 10 ).
The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's results surpass the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.
Pi Approximation Day is observed on July 22 (22/7 in the day/month date format), since the fraction 22 ⁄ 7 is a common approximation of π, which is accurate to two decimal places and dates from Archimedes. [33] In Indonesia, a country that uses the DD/MM/YYYY date format, some people celebrate Pi Day every July 22. [34]
The word is a play on the word "pi" itself and of the linguistic field of philology. There are many ways to memorize π , including the use of piems (a portmanteau , formed by combining pi and po em ), which are poems that represent π in a way such that the length of each word (in letters) represents a digit. [ 1 ]
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