DailyDirt: Pi Math

from the urls-we-dig-up dept

National Pie Day is not actually March 14th (although it really should be, if only to make it more memorable). But here's to the number, not the delicious dessert. If you'd like to read more awesome and interesting stuff, check out this unrelated (but not entirely random!) Techdirt post.

Filed Under: calculations, irrational, math, numbers, pi

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  1. identicon
    Anonymous Coward, 15 Feb 2013 @ 5:18am

    if you have a random distribution of 100 numbers (0 to 9) each of those 100 positions has a 10% chance of containing any of those positions. I is possible (not probably) that you will roll 100 random numbers (0 to 9) and never have the number 1 occur. But generally with a random distribution you would expect about 10 1's to occur (10% of 100).

    so make your start number 1000 numbers in length, and you can expect on average 100 1's 2's .. 0's to occur approx. 100 times each.

    Yes, it is still possible to roll your 0-9 dice 1000 times and never get a 1, but probably not.

    out of those 100 1's or 2's or 3's you get from your list of 1000 numbers you have a 10% chance that the following number will be 0 to 9. so with 100 occurrences of any 1 number you have 100 x 10% chance of getting and complete 2 digit sequence.

    so therefore sooner or later in a very long sequence of randomly distributed numbers you will get any one specific sequence. What is necessary is your initial number length is enough.

    what is surprising to me is how SMALL a string of randomly distributed numbers are to achieve an extremely high to 100% probability of a sequence to occur.

    like what are the odd's of rolling your 10 dice and getting 9 '8s' in a row !!!.

    But it occurs in pi at around 50 million decimal places !!

    you get 0 to 9 dice and roll them 50 million times and you might roll 8 '0s' too.

    everything does and will occur if you do it long enough.

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