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I explored the value of PI up to 10 million digits with the following link

http://pi.karmona.com/

From here I realized that it included many scientific constants. Below are some examples

• …1618033… Where 1.618033 ~ golden ratio to be used in design, painting, and architecture etc. (Source: http://mathworld.wolfram.com) • …271828… Where 2.71828 ~ Euler’s number (Source: http://mathworld.wolfram.com) • …667408… Where 6.67408 ~ constant of gravitation (Source: http://physics.nist.gov) • …8987… Where 8.987 ~ Coulomb constant in electrostatic (Source: http://scienceworld.wolfram.com/physics) • …885418… Where 8.85418 ~ electric constant (Or Vacuum permittivity) (Source: http://physics.nist.gov) • …6626070… Where 6.626070 ~ Planck constant (Source: http://physics.nist.gov) • …16021766… Where 1.6021766 ~ elementary charge (Charge of electron) (Source: http://physics.nist.gov) • …9109383… Where 9.109383 ~ electron mass (Source: http://physics.nist.gov) • …980665… Where 9.80665 ~ acceleration of gravity (Source: http://physics.nist.gov) • …602214085… Where 6.02214085 ~ Avogadro constant (Source: http://physics.nist.gov) • …1380648… Where 1.380648 ~ Boltzmann constant (Source: http://physics.nist.gov) • …167262… Where 1.67262 ~ Proton mass (Source: http://physics.nist.gov)

And maybe there are more cases. I wonder this interesting finding is only accidental, or there is any implicit rule here.

Any feedback or discussion can be sent to [email protected] It’s nice if you can share my article in social media for more opinions

Thinh Nghiem

Thinh Nghiem
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  • Looks more like a coincidence. There are like billions of possibilities with a number / symbol which ain't really ending. You never know when you may out of a plethora of combinations which this number offers. Pardon me If 'm wrong. M just an intermediate student :) – The Dead Legend Apr 20 '17 at 13:03
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    In any randomly generated string of $10^7$ decimal digits, a given $7$-digit string has probability $\approx 1 - e^{-1} \approx 0.63%$ of occuring at least once. If one checks many strings of this length or shorter, one will sure find many appearances in total. – Travis Willse Apr 20 '17 at 13:03
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    Try looking at the decimal expansion of, say $\sqrt{2}$. My guess is you'll find the same stuff there.There's lots of mysticism falsely attributed to $\pi$. – MPW Apr 20 '17 at 13:04
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    The links you provide above have no bearing on where one might locate the indicated consecutive digits ("many scientific constants") in the first million digits of $\pi$. It is an unproven conjecture, noted here at Math.SE many times, that $\pi$'s decimal expansion eventually produces all possible consecutive digits of finite length. – hardmath Apr 20 '17 at 13:04
  • @hardmath Is there a proof of having such property for any number that is not constructed specifically for this purpose? – Evgeny Apr 20 '17 at 13:09
  • @Evgeny: Although almost all numbers have this property, it is certainly true that numbers which are explicitly known to have it are contrived examples. Some "uncomputable" numbers are known to be normal numbers. – hardmath Apr 20 '17 at 13:14
  • Some of your strings are 6 digits, some 7, one only 4. It sure feels like you're finding what you're looking for by ignoring any evidence against your conjecture. Did you look for any other constants and not find them? – Arby Apr 20 '17 at 13:31
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    Not only do the digits of pi contain the first few digits of scientific constants, but it also contains digits of "non-scientific constants." Try looking for your telephone number, your student number, and so on. Amazing! – JRN Apr 20 '17 at 14:06
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    one thing that tends to reduce the chances of this having any profound meaning, is that many of the physical constants depend on measurement systems that are pretty much arbitrary human constructs - for example a metre could have been any other distance, what if a metre had been defined differently? Similalry with other units, second, Kg etc. – Cato Apr 20 '17 at 14:17

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With the Pi-Search Page you can search the first $200$ million digits of $\pi$. I searched for $62831853$, which you may or may not recognize as $\lfloor 2 \pi 10^7 \rfloor$. I also searched for my credit card number and CVN, but of course I'm not going to disclose those here. I will tell you that I did find them in the digits of $\pi$.

On a slow news day, news organizations might write articles about this, and they have in the past. Here's one from Inquirer.net. There is no particularly deep significance to this, just a quick way to generate copy for the Sci/Tech section of the paper when we go too long without discovering a new Mersenne prime.

Now, the really interesting question is: do the base $10$ digits of $\pi$ contain as substrings all positive integers? That's a question that has been asked on this website, but as yet no one knows the answer to that.

Mr. Brooks
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