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Question #19903. Asked by **m**.

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24 year member

1512 replies

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pi, in mathematics, the ratio of the circumference of a circle to its

diameter. The symbol for pi is . The ratio is the same for all circles and is

approximately 3.1416. It is of great importance in mathematics not only in

the measurement of the circle but also in more advanced mathematics in

connection with such topics as continued fractions, logarithms of imaginary

numbers, and periodic functions. Throughout the ages progressively more

accurate values have been found for {;} an early value was the Greek

approximation 3 1/7, found by considering the circle as the limit of a series

of regular polygons with an increasing number of sides inscribed in the

circle. About the mid-19th cent. its value was figured to 707 decimal places

and by the mid-20th cent. an electronic computer had calculated it to

100,000 digits. It would have taken a person working without error eight

hours a day on a desk calculator 30,000 years to make this {calculation;} it

took the computer eight hours. Although it has now been calculated to more

than 100,000,000 digits, the exact value of cannot be computed. It was

shown by the German mathematician Johann Lambert in 1770 that is

irrational and by Ferdinand Lindemann in 1882 that is {transcendental;}

i.e., cannot be the root of any algebraic equation with rational coefficients.

The important connection between and e, the base of natural logarithms,

was found by Leonhard Euler in the famous formula ei=-1, where i=.

http://www.infoplease.com/ce6/sci/A0838910.html

diameter. The symbol for pi is . The ratio is the same for all circles and is

approximately 3.1416. It is of great importance in mathematics not only in

the measurement of the circle but also in more advanced mathematics in

connection with such topics as continued fractions, logarithms of imaginary

numbers, and periodic functions. Throughout the ages progressively more

accurate values have been found for {;} an early value was the Greek

approximation 3 1/7, found by considering the circle as the limit of a series

of regular polygons with an increasing number of sides inscribed in the

circle. About the mid-19th cent. its value was figured to 707 decimal places

and by the mid-20th cent. an electronic computer had calculated it to

100,000 digits. It would have taken a person working without error eight

hours a day on a desk calculator 30,000 years to make this {calculation;} it

took the computer eight hours. Although it has now been calculated to more

than 100,000,000 digits, the exact value of cannot be computed. It was

shown by the German mathematician Johann Lambert in 1770 that is

irrational and by Ferdinand Lindemann in 1882 that is {transcendental;}

i.e., cannot be the root of any algebraic equation with rational coefficients.

The important connection between and e, the base of natural logarithms,

was found by Leonhard Euler in the famous formula ei=-1, where i=.

http://www.infoplease.com/ce6/sci/A0838910.html

Jun 16 2002, 11:20 PM

Answer has

24 year member

1331 replies

Answer has

Pi is not infinite. It is finite, having a value less than 4. It does however have an infinite number of decimal digits, if it is written out in decimal notation 3.1415927... This is true of all irrational numbers, of which there are many. It also is called 'transcendental' which means it is not the solution to any simple equation with rational coefficients.

Jun 17 2002, 11:40 AM