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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?

GNUSupporter 8964民主女神 地下教會
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abdelrahman taher
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    Please tell us what is this algorithm. – E. Joseph Dec 29 '16 at 13:05
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    If its a big deal for you, it could be a big deal for me, and we're a big deal to you, hopefully you'll join us all on MSE and do more maths like this. – Simply Beautiful Art Dec 29 '16 at 13:05
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    The probability that you rediscovered something well-known is one, sorry. –  Dec 29 '16 at 13:05
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    It may be small step for mankind but a giant leap for you. Keep on being curious! – Hirek Kubica Dec 29 '16 at 13:07
  • I am sorry is it safe to publish it here (just if it's really important) – abdelrahman taher Dec 29 '16 at 13:08
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    If your way is faster than modern methods, then it'd be a big deal! However, to test this you'll have to use multiple precision software instead of Excel. – lhf Dec 29 '16 at 13:09
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    Can you please share the Excel file with us? While it might not be that big of a deal since it's only 15 digits, I am always interested in alternative algorithms and at the very least, it could teach us something. Also, we promise not to discourage you for your efforts or steal credit. – Noble Mushtak Dec 29 '16 at 13:09
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    @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. – Simply Beautiful Art Dec 29 '16 at 13:11
  • There are many many ways to compute $\pi$ and the most interesting formulas are those that allow to compute a huge amount of decimals in reasonable time. (The current record is 10 000 billion decimals.) –  Dec 29 '16 at 13:11
  • Though note that any text published here is licensed under CC-BY-SA. – Patrick Stevens Dec 29 '16 at 13:12
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    @YvesDaoust Why not 10 trillion? – Simply Beautiful Art Dec 29 '16 at 13:13
  • The book Pi: A Source Book by Berggren, Borwein, and Borwein might be interesting for you. – hardmath Dec 29 '16 at 13:13
  • just one thing i don't kniw how to put a file here – abdelrahman taher Dec 29 '16 at 13:13
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    @SimpleArt: British and American namings differ. –  Dec 29 '16 at 13:14
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    There is no way to put a file here, so @NobleMushtak's suggestion is not practical unless you were able to host the file on another site and put the link in you post here. It would be better to simply explain/describe your algorithm (not share an Excel file), in my opinion. – hardmath Dec 29 '16 at 13:16
  • Upload your Excel file to Google Drive and then follow the instructions here under "Sharing a link". Once you have the shareable link, post it in a comment. – Noble Mushtak Dec 29 '16 at 13:16
  • My idea is simply about getting the approximation of the area of the circle then dividing it by the square root of the radius – abdelrahman taher Dec 29 '16 at 13:23
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    @abdelrahmantaher It's already been done here. – Simply Beautiful Art Dec 29 '16 at 13:24
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    @abdelrahmantaher It seems like you'll want to teach yourself calculus, that's the road that you are treading. – Simply Beautiful Art Dec 29 '16 at 13:25
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    Early approximations of $\pi$ were obtained by approximating circles with regular polygons, by doublings (3rd century BCE). For some reason, they didn't use Excel, though :) –  Dec 29 '16 at 13:29
  • i am sorry i don't understand this advanced math.But anyway my idea is drawing a square in a circle then at then use each side ot this square as a base for an isosceles triangle and then using the 2 eqaul sides of this triangle to draw an isosceles triangle and so on..... – abdelrahman taher Dec 29 '16 at 13:30
  • @abdelrahmantaher Basically what YvesDaoust was saying I think. – Simply Beautiful Art Dec 29 '16 at 13:31
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    Even if the method exists, congratulations ! – Claude Leibovici Dec 29 '16 at 13:32
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    You will find interesting historical material about that quest here: https://en.wikipedia.org/wiki/Approximations_of_%CF%80 –  Dec 29 '16 at 13:34
  • @abdelrahmantaher Sounds like Archimedes method of approximation, check this video https://www.youtube.com/watch?v=_rJdkhlWZVQ . – Sil Dec 29 '16 at 13:36
  • so is it right anyway – abdelrahman taher Dec 29 '16 at 13:36
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    Ofc it is, its perfectly fine :D Relatively simple too, no? But if you are so interested, you could learn other techniques to approximate $\pi$ or just math in general. – Simply Beautiful Art Dec 29 '16 at 13:39
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    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 – abdelrahman taher Dec 29 '16 at 13:41
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    All math nerds were expecting something new xD – Fawad Dec 29 '16 at 13:44
  • abdelrahman, so you were doing something like this, then? That precisely is Archimedes's procedure. – J. M. ain't a mathematician Dec 29 '16 at 15:32
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    Good for you :-) No matter what your algorithm is, it's great that you can do that :-) – Matt Gutting Dec 29 '16 at 16:02
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    Great work! Now, for faster convergence, consider both the inscribed polygon (your current approach) and the circumscribed polygon. Find both areas and average. This is a very real application of the "sandwich theorem". – Prune Dec 29 '16 at 17:39
  • First of all: congratulations! I completely agree with 5xum's answer. I can only recommend you to train yourself in using more powerful tools for math (like R, Matlab, Haskell, etcétera). You have the right mixture of creativity, curiosity and skill to be great at math. – Barranka Dec 29 '16 at 21:50

2 Answers2

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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!

5xum
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    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 $\pi$. –  Dec 29 '16 at 13:18
  • @YvesDaoust There is no way for me to object with Taylor's theorem? – Simply Beautiful Art Dec 29 '16 at 13:19
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    @SimpleArt: using Taylor you lose all the benefit of the fast convergence. –  Dec 29 '16 at 13:22
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    Thank you for encouraging this person's creativity. It probably helps more than you know! – ijustlovemath Dec 29 '16 at 15:13
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    @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 $\pi$. – J. M. ain't a mathematician Dec 29 '16 at 15:19
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    @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. –  Dec 29 '16 at 15:28
  • @Yves, "the computation of $\sin$ requires the knowledge of $\pi$", as you said, but CORDIC computes the function fine without knowing about it. Again, I agree that this is not practical as a computation method for $\pi$; I'm just pointing out the incompleteness of your first comment. – J. M. ain't a mathematician Dec 29 '16 at 15:31
  • @J.M.isn'tamathematician: that's a nonsense. The effort required to compute the constants in CORDIC is much larger than the effort to just compute $\pi$ (and there are much fewer methods to obtain them). In fact these constants are very close to the approximations appearing in the Archimedean method of polygon duplication. So before being able to compute $\pi$, you must compute... $\pi$. –  Dec 29 '16 at 15:34
  • I'm not disagreeing @Yves about the impracticality (maybe my English is not getting through? should I rephrase?), I was taking issue about "requires the knowledge of $\pi$", which is absurd. Yes, I agree that computing the required constants for CORDIC is just as difficult as computing $\pi$ itself. – J. M. ain't a mathematician Dec 29 '16 at 15:38
  • @J.M.isn'tamathematician: I forgot to mention that CORDIC requires a quadrant reduction, which necessitates the knowledge of... $\pi$. –  Dec 29 '16 at 15:41
  • Can you tell us the basis for your algorithm / equation and how you derived it? – paparazzo Dec 29 '16 at 20:28
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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.

djechlin
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