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'''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.   

'''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).

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<ref>{{cite web

| accessdate = 2012-02-12}}</ref> proved this in 1761 by showing that '''π''' is an [[irrational number]]; Lindeman<ref>{{cite web

| accessdate = 2012-02-12}}</ref> 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.

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.