I am a 15 year old teen and fond of mathematics. I always try to prove mathematical theories and I tried to find how to get pi using an algorithm. Then I found out a way and made an algorithm and inserted it in an Excel sheet and it gave out the first 15 digits after the decimal sign. I just want to know if this is a great deal?

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    $\begingroup$ Please tell us what is this algorithm. $\endgroup$ – E. Joseph Dec 29 '16 at 13:05
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    $\begingroup$ The probability that you rediscovered something well-known is one, sorry. $\endgroup$ – Yves Daoust Dec 29 '16 at 13:05
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    $\begingroup$ It may be small step for mankind but a giant leap for you. Keep on being curious! $\endgroup$ – Hirek Kubica Dec 29 '16 at 13:07
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    $\begingroup$ @abdelrahmantaher Its totally safe. Once you put it out there, we can't remove it and claim its ours ( unless we actually found it first :-/ ), and I don't think anyone's gonna hack your account just for a $\pi$ algorithm. My grandma makes me good enough apple $\pi$ already. $\endgroup$ – Simply Beautiful Art Dec 29 '16 at 13:11
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    $\begingroup$ Thank you all who participated in this discussion this is actually the firt time for me for discussing something on a forum but it turns out it's helpful $\endgroup$ – abdelrahman taher Dec 29 '16 at 13:41

We can't really say much about your algorithm because we don't know it. I think it's perfectly safe to post it on this site, as even if someone tries to "steal" your algorithm and publish before you do, you will have pretty solid evidence that you, in fact, made the original discovery.

However, based on statistics alone, the two most likely options are

  1. The algorithm already exists.
  2. The algorithm is wrong.

If the algorithm already exists, then congratulations. Being able to reproduce an existing piece of research on your own at such a young age is amazing! Sure, it may not be someting new yet, but it proves you have a creative brain that will, one day, probably discover something new.

If the algorithm is wrong, then congratulations. Being able to think in new ways, even if they are wrong, is a great talent to have. In time, when you add more knowledge to the mix, you will be able to filter out wrong ideas even further, but thinking of an algorithm proves, again, that you have a creative mind. Keep working, and you'll get far!

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    $\begingroup$ A good example of a wrong solution is given by the iteration $x_{n+1}=x_n+\sin(x_n)$, which indeed converges to $\pi$ very fast from $x_0=1$. But this is of no use as the computation of the sine requires the knowledge of $\pi$. $\endgroup$ – Yves Daoust Dec 29 '16 at 13:18
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    $\begingroup$ @SimpleArt: using Taylor you lose all the benefit of the fast convergence. $\endgroup$ – Yves Daoust Dec 29 '16 at 13:22
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    $\begingroup$ Thank you for encouraging this person's creativity. It probably helps more than you know! $\endgroup$ – ijustlovemath Dec 29 '16 at 15:13
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    $\begingroup$ @Yves, I don't remember CORDIC needing the knowledge of $\pi$... but I agree that using Newton-Raphson is not the most practical method for $\pi$. $\endgroup$ – J. M. isn't a mathematician Dec 29 '16 at 15:19
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    $\begingroup$ @J.M.isn'tamathematician: I didn't mention CORDIC nor Newton-Raphson. CORDIC is certainly not appropriate, it requires the knowledge of $n$ precomputed trigonometric constants as hard to compute as $\pi$, where $n$ is the number of desired decimals. $\endgroup$ – Yves Daoust Dec 29 '16 at 15:28

I would probably start by trying to determine if your formula is a rediscovery of a known formula. Wikipedia seems quite enthusiastic about this question.

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