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Pi or p is a mathematical constant whose value is
the ratio of any circle's circumference to its diameter in Euclidean
space; this is the same value as the ratio of a circle's area to the
square of its radius. It is approximately equal to 3.14159 in the
usual decimal notation (see the table for its representation in some
other bases). p is one of the most important mathematical and
physical constants: many formulae from mathematics, science, and
engineering involve p.
p is an irrational number, which means that its
value cannot be expressed exactly as a fraction m/n, where m and n
are integers. Consequently, its decimal representation never ends or
repeats. It is also a transcendental number, which means that no
finite sequence of algebraic operations on integers (powers, roots,
sums, etc.) can be equal to its value; proving this was a late
achievement in mathematical history and a significant result of 19th
century German mathematics. Throughout the history of mathematics,
there has been much effort to determine p more accurately and to
understand its nature; fascination with the number has even carried
over into non-mathematical culture.
The Greek letter p, often spelled out pi in
text, was adopted for the number from the Greek word for
perimeter, first by William Jones in 1707, and popularized by
Leonhard Euler in 1737. The constant is occasionally also
referred to as the circular constant, Archimedes' constant (not to
be confused with an Archimedes number), or Ludolph's number (from a
German mathematician whose efforts to calculate more of its digits
became famous). |