Onepintcan has taken exception to me for stating that pi is not 22/7. However, using 22/7 in place of pi will produce acceptable results in many cases because it is a useful approximation.
More accurate values of pi can be calculated using various infinite series. However, since it is irrational, one can never get an exact value. I never claimed to have an exact value, but some useful series have been posted here to enable the calculation of good approximations. (much better than 22/7).
One such series is:
4/1 - 4/3 + 4/5 - 4/7 + 7/9 ...... and so on.
This is an infinite series whose sum would reach pi after an infinite number of terms. It is easy to continue the sequence: the numerators are all 4, the denominators are all odd, increasing by 2 each time, and the sign (+/-) alternates.
The more terms you use, the greater the accuracy. However, it does take quite a large number of terms before it achieves an acceptable level of accuracy.
Is this an acceptable answer?
2007-06-24
01:55:45
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15 answers
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asked by
Nick J
4
in
Mathematics