Why this fuss about Pi, Onepintcan?

Question

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?

This will be the end of the bitching, I promise! I'm assuming people who participate in this category are actually interested in Math, which is why I still find it amazing that some people never seem to accept that they are mistaken about 22/7.
22/7 to 4 decimal places is 3.1429
pi to 4 decimal places is 3.1416.
See the difference?

Onepintcan - you are now saying that 22/7 is an approximation. Of that, we agree. However, your post which got deleted seemed to indicate you believe it to be exactly 22/7.

Also, you say I claimed to have an answer. All I said was that I would have answered another question, but didn't because someone else had already given a correct answer. I have now given an answer in the main text of this question, as requested.

Finally, there are 2 ways your original answer could have gone missing - either you edited it yourself, or a moderator deleted it. I certainly couldn't have done it.

Answer 1

Onepintcan, the fact that π is irrational does not mean that 22/7 is as useful as any other approximation (for instance, it is useless in any application where you need more than 3 significant digits of accuracy). More to the point, it does not address his point that π is not actually equal to 22/7, which you actually PROVE by your point that π is irrational (since 22/7 is rational and π is not).

Also, I find it funny that you would state that Nick deleted your post. Actually, on second thought, I don't find that funny, I find that to be malicious libel. It is physically impossible for Nick to have deleted your post, whereas it is physically possible for Y!A to have deleted your post because it was in violation of community guidelines (the fact that your post allegedly wasn't abusive is irrelevant -- Y!A can and has in the past removed perfectly innocent posts, and if you go over to the comments and suggestions board, you will find "my post was wrongfully deleted" to be by far the most common complaint). That said, it appears to be a database glitch (I say this because Emma T's post was also deleted, and subsequently restored), which is also quite common (happened to Puggy some time ago - he was wrongfully removed from his position on the leaderboard because he edited his profile).

Nick - I'm sorry you have suffered so much grief at the hands of onepintcan and his yes-men (Bob S and Gandalf). I'm not too familiar with them, but I know that this is not the first time that onepintcan has greatly misinterpreted someone's question and proceeded to heap abuse on them, and you are not being unreasonable to be frustrated at the fact that so many people do believe that 22/7=π (see, for instance, Professor Monkey's answer). Please, don't let their reaction stop you from continuing to insist on correct mathematics.

Answer 2

I agree with you. 22/7 is an approximation, but not one I have ever used because I have always had a calculator with a pi button. 22/7 is actually a pretty poor approximation, as it starts to diverge from the value of pi after just a few decimal places. I agree with you that no-one can ever have an exact value for pi due to it's irrational nature, but pi has been worked out to several million decimal places which should be accurate enough for almost anyone. If one more person says pi = 22/7, I might scream! It does not!

Answer 3

The above is a better approximation when we take a finite number of terms and 22/7 and also 355/133 are other appoximations but there are better series approximations for the same. Why it is a value this is based on the following link

Answer 4

My first thought was to stay out of this because nick obviously has a problem. However on reflection I feel that I have to defend myself.

In the original question/my answer to same, the asker decided to take one small part of my answer, that was that 22/7 is about as much use as any other calculation and a handy one if you are doing the calculation mentally.

Some how my original answer was deleted, I don't think Yahoo did it because there was certainly no abuse in the text. From the comments here some people must have read my original answer.

My later question asked nick how he deleted my text/answer. (see Bob s links).

I repeat nick. You stated that you had the correct answer to PI state it or get out of the game!

Answer 5

The infinite series 4 - 4/3 + 4/5 - ... does equal pi after an infinite number of terms, it is called Gregory-Leibniz series, but it does take quite a few terms in that series to get to 3.14. (after 1000 terms of that, it is to: 3.14259165)

There are other formulas for calculating pi, for instance:
lim
x → ∞       x * sin(180° / x) * cos(180° / x)

There are more formulas for calculating pi on wikipedia ( http://en.wikipedia.org/wiki/Pi#Analysis )

(Also, to Professor Monkey, if you divide 22 by 7, you will not get pi. (see link for 22/7 value: http://www.google.com/search?q=22/7 ) You will get 3.14285... where pi is 3.14159... You could also look at this page on wikipedia, proof that 22 over 7 exceeds pi. http://en.wikipedia.org/wiki/Proof_that_22_over_7_exceeds_%CF%80

Answer 6

Onepintcan did not take exception to you stating that 22/7 was incorrect. He quite rightly pointed out that it was no better than any other Pi calculation and that there will never be a definitive conclusion to Pi calculations. In your original question you stated that you had the correct answer to Pi onepintcan has asked repeatedly for you to post the answer.

Answer 7

you should tell onepintcan about this personally not evryone else!
(p.s. pi is irrational so 22/7 will not give you the exact amount,
but it works well as a good approximation!)

Answer 8

'I have looked at this and the two questions in Bob s links. I can still see onepintcan's original answer, Thats maybe because I use Linix and Firefox. It seems to me that he provided a good structured argument and that you, nick decided to pick one part of his answer, completely out of context I might say and then use it as an excuse to vilify him,"onepintcan that is". I have also looked at onepintcan's other answers and I conclude that he provides good advice and certainly does not abuse anyone. As someone else said GO GET A LIFE.

Answer 9

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Answer 10

You seem to be making all the fuss and have conveniently forgotten the subject of your original question, (see Bob s first source link). Emma T if you think your calculator is any good then find the square root of 10 multiply it by its self. The answer won't be 10. If you understand that you will appreciate onepintcans answer to the original question.