Palindrome *The pattern of number pi.

[Don McDonald]

    date: Fri 07-Sep-2001, 8-9-01, 23.03.03.
     
    myfile.>  DON01. fin soc AcornCp 
    Usr.DonWn994/2.pi. S/ piSearch 

Dear Brian Stokes, NZMM, sequence fans.
    your magaz./ regds Don McDonald.
     
    If the decimal expansion of pi 
    (=3.14 159...) contains  7x 
    consecutive 9s somewhere, we could 
    just about round it off there to a 
    terminating fraction ooo,oooo. 
    (Menzed Mensa NZ Iss.#370,Sept2001) 
     
    So the computer Internet website, 
    www.angio.net/pi  (search: 
    Pi-Search Page, joyofpi, etc.) 
    allows anyone - if you can call 
    Google search engine- to enter up 
    to 10 digits (particularly such as 
    a birthdate..) The computer should 
    then report if and exactly where 
    your sequence may occur within the 
    first 100-million digits of pi. 
     
    When I did that at National Library 
    of N.Z., I soon found (in about 1 
    second) 7x consecutive 9s in a 
    segment of pi of 14x consecutive 
    odd digits, followed immediately by 
    11 consecutive even digits.** 
    That is 25 successive digits with 
    only one switch between odd or 
    even. (Think of them like as 14 
    Heads and 11 Tails, or 14 wet years 
    followed by 11 dry years! newgroups 
    :nz.general) 
     Note that the 14 odd digits con- 
    tain a 13 digit decimal palindrome 
    (spelt the same forwards/ as 
    backwards.) 
     
    9 713 999 9999 317  66 88 42  000 
    64. 
     
    (...At position 1722 776 counting 
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    from the first digit after the 
    decimal point.  The 3. is not 
    counted.) Is it  Remarkable?

Later. Compare. Sqrt(10) = 3.1622776601 by hand.
     
    Pi is NOT a RATIONAL number, the 
    ratio of 2 whole numbers.  
    Contrast 0.14 28 57 1428 57..../ 
    point .999 999 999 999... 
    = 142857/999999 = 1/7. I am told 
    this is part of second year 
    university work. 
     
    Hence pi can never repeat with a 
    fixed decimal period. 
    But does pi perhaps start over...  
    '314 159' somewhere? 
     
    Indeed so. It appears this short 
    piece of pi repeats (not 
    indefinitely of course) at position 
    125 9351. (Pi-Search Page.)  The 
    actual digits are. 
    xx  3141, 59 948 7777 678 77... 
    The 'sevens digits' are frequent. ...
     
    What is the average decimal digit 
    of pi? We expect 4.5. 
    (..Is pi 'normal?'; this is an 
    unsolved problem). If each digit is 
    equiprobable then the limiting 
    average of 0-9 is always 4.5. (E.g. 
    In pairs 09, 18, 27,36,45.) 
     
    A curiosity I have noted is that, 
    calculating the average of 2,3,4,5, 
    digits etc. beginning right there 
    after 3141,  5+9 above, gives run- 
    ning mean 7 (9 times in a row of 
    when the answer is an exact 
    integer.) 
     
    Check sums = 5,14/2,23/3,27/4, 35/ 
    5,...42/6,49,56,63, 69,76,84,91,98. 
     
    Running means: 57..7 7777 ..777.  
    (I display dot '.' whenever the 
    average is not a whole number.) 
     
    This is a/nother beautiful pattern? 
     
    /  Don S. McDonald  #1048.  
    (Wellington, New Zealand)  
      
    voice  64  ( 4)-   389 6820.  
    F 63/3 Hutchison Rd, Wellington.
    New Zealand. 
     
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    Editor Menzed, ** Dear Sue G,