Are there patterns in Pi?

  1. or is it all random? thanks :approve:
     
  2. jcsd
  3. phinds

    phinds 8,333
    Gold Member

    Well given that it goes on for an infinite number of digits you are bound to find random sets of seemingly repetitive strings of digits but in the sense that I suspect that you mean it is purely random. If it ever started to repeat one string of digits forever then it would be a rational number, but it is not ... it is irrational.
     
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  4. jedishrfu

    Staff: Mentor

    My favorite is the Carl Sagan speculation in his sci-fi novel Contact, that PI has embedded within its infinite digits the image of a circle how ever you choose the interpret the digits.

    There's a lot of creative PI art that can be found via Google Image search "PI art" and here's a couple of links:

    http://www.google.com/url?sa=i&rct=...fZRp8zgfqIRGqQtj8f_Jk-lQ&ust=1400951799993306

    http://www.google.com/url?sa=i&rct=...fZRp8zgfqIRGqQtj8f_Jk-lQ&ust=1400951799993306

    but no circle's been found yet.
     
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  5. D H

    Staff: Mentor

    You are essentially asking whether pi is a normal number. Whether it is or isn't is unknown. It's very hard to prove whether a number is normal.

    Consider the following base 10 number: 0.101001000100001000001... This number is irrational, but it is not normal.
     
  6. Matterwave

    Matterwave 3,816
    Science Advisor
    Gold Member

    1 person likes this.
  7. adjacent

    adjacent 1,533
    Gold Member

  8. LCKurtz

    LCKurtz 8,278
    Homework Helper
    Gold Member

    That site says ##\pi## is an infinite non-repeating decimal "meaning that every possible number combination exists somewhere" in the decimal expansion of ##\pi##. No, that means that ##\pi## is irrational. Whether it satisfies that phrase in quotes is an open question.
     
  9. micromass

    micromass 18,536
    Staff Emeritus
    Science Advisor

    Yes. The link provided by adjacent contains a lot of misinformation. I'm only leaving the post up because the link is very popular on the internet, so it would be good to debunk it here. So all the readers should be aware that it is very problematic.
     
  10. adjacent

    adjacent 1,533
    Gold Member

    Pi is irrational, is it not?

    Would you mind explaining why it's problematic and contains misinformation?
     
  11. A sequence of decimal digits can be non-repeating without having to contain all possible subsequences.

    For instance, 0.101001000100001... is irrational. It's decimal expansion never repeats. But its decimal expansion also does not contain any 2's.
     
  12. jedishrfu

    Staff: Mentor

    Stating some number is irrational means that it is not rational ie you can't define it as the ratio p/q of two integers p and q where q not equal to zero.

    Taking that as a definition you can't leap to the conclusion that all possible combinations of digits will appear.

    As an example, you could get a non-repeating sequence of digits without the digit 9 appearing anywhere in the sequence and still have an irrational number but not with every combination of digits.
     
  13. adjacent

    adjacent 1,533
    Gold Member

    We already know that Pi contains numbers from 0 to 9. So that means it's proved.
     
  14. @adjacent - take 1/90 and add 0.2 to it, does that number have any arbitrary length of the string of 2's in it? Using your logic, it must - despite all indications to the contrary. And I could do the same thing with 1/900 and 0.23 or 1/9000 and 0.234...should I draw a map? Yes, I know that this continuing fraction isn't transcendental. Extending this simple argument to 0.101001etc. is not exactly rocket science.
    -=-=-
    On a more interesting note: @acesuv: take a look here for some patterns in π:
    https://en.wikipedia.org/wiki/Generalized_continued_fraction#.CF.80
    -=-=
    the whole continued fraction thing is just fascinating...
     
    Last edited: May 28, 2014
  15. micromass

    micromass 18,536
    Staff Emeritus
    Science Advisor

    The number 0.123456789010010001000010000010... is also irrational and contains numbers from 0 to 9. It still doesn't satisfy the property you want.
     
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  16. adjacent

    adjacent 1,533
    Gold Member

    I think that the author of the [STRIKE]post[/STRIKE] image meant that a digit can be used as many times you want. He must have thought without considering the reality.
    :biggrin:
     
    Last edited: May 28, 2014
  17. micromass

    micromass 18,536
    Staff Emeritus
    Science Advisor

    Exactly. And it is currently unknown that every digit in ##\pi## occurs as many times as you want.
     
  18. HallsofIvy

    HallsofIvy 40,308
    Staff Emeritus
    Science Advisor

    That means what is proved?

    What post are you talking about?
     
  19. adjacent

    adjacent 1,533
    Gold Member

    It is proved that you can have all the combinations of digits.( I have just realised that this is wrong)
    Sorry,not the post. The image.
     
  20. jedishrfu

    Staff: Mentor

    Ahh, the life of Pi, some people get eaten by tigers and some not so much.
     
  21. adjacent

    adjacent 1,533
    Gold Member

    What do you mean? I don't understand.
     
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