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'''Pi''' (<big><math>\pi</math></big>) is the ratio of the circumference of a circle to its diameter. The value of <big><math>\pi</math></big> is both an [[irrational number]] and a [[transcendental number]]; which means that it cannot be fully expressed as a fraction or a decimal (regardless of the number of digits used), nor can it be expressed as the solution to any polynomial equation with rational coefficients. To five decimal places, <big><math>\pi</math></big> <big><math>\approx</math></big> 3.14159. Using the convention that Greek letters in mathematics have conventional meaning, the ratio takes its name from the sixteenth letter of the [[Greek alphabet]]. It is an important number and appears in many [[mathematical]] and [[physics|physical]] formulae.
'''Pi''' or '''<big><math>\pi</math></big>''' or '''π''' is the name or symbol for an important mathematical constant, which appears in many branches of [[mathematics]]. '''π''' was originally defined in geometric terms as the ratio of the circumference of a circle to its diameter. A simple well-known formula using '''π''' gives the area of a [[circle]] as: '''π''' * radius * radius.
An approximate value for '''π''' is 3.141592653... The exact value can never be expressed as a fraction or as a decimal number, regardless of how many digits are used (Lambert proved this in 1761 by showing that '''π''' is an [[irrational number]]; Lindeman went further in 1882 and proved that '''π''' is a [[transcendental number]] which means it can't be expressed as the solution to any simple equation).
The approximate value quoted above is accurate enough to calculate the circumference of a circle of the size of the Earth with an error of only about 1 millimetre. For rough approximations, the fraction 22/7 (= 3.142857...), correct to 2 decimal places, is sometimes used. A more accurate fractional approximation is 355 / 113 (= 3.14159292), which is correct to 6 decimal places.
==History==
==History==
The Greek letter π is the sixteenth letter of the [[Greek alphabet]]. It was first used with its current meaning in 1706 by a Welsh mathematician William Jones because it is the first letter of the Greek word for [[perimeter]].
Mathematicians have worked for centuries to calculate <big><math>\pi</math></big> to more and more decimal places. To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.
Mathematicians have worked for centuries to calculate <big><math>\pi</math></big> to more and more decimal places. To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.