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This isn't true in a strict sense, is it? The digits of pi aren't random, and for numbers of arbitrary size, it seems that you could just keep asking for a long
by pingswept 17y ago
This isn't true in a strict sense, is it? The digits of pi aren't random, and for numbers of arbitrary size, it seems that you could just keep asking for a longer numbers until you can't find a match any more.
Ah, we know that none of the numbers of the form pi + x can found in pi.
But I still wonder whether there exist numbers of finite length that can't be found within the digits of pi. Any hardcore mathematicians in the house?
- brown9-2 17y agoRelated: http://www.angio.net/pi/whynotpi.html http://www.angio.net/pi/whynotpi.html
- DeusExMachina 17y agoI'm not a mathematician, but I read a lot of time ago that since pi is infinite but not periodic, you shold be able to find in it any sequence you want, given infinite time to search in it. This is what I remember, but I could be wrong.
- zackattack 17y agoYou can't find 1/9 in pi. 1/9 precludes the possibility of any other sequence.
- staticshock 17y agoI think the parent was talking about sequences of digits, i.e. integers, not just "any rational number"
- deleted 17y ago[deleted]
- alphaBetaGamma 17y agoThe statement (infinite && not periodic) ==> (any finite sequence is in it) is not true. \a number could have a decimal expansion that is not periodic but does not include certain digits. E.g: write Pi in binary and consider the same sequence of 0's and 1's as a number in decimal
- Oatmeat 17y agoIt is conjectured that pi is normal: http://en.wikipedia.org/wiki/Normal_number http://en.wikipedia.org/wiki/Normal_number If the conjecture is true then any finite sequence of numbers can be found in the digits of pi. As others have noted, infinite sequences are not guaranteed or even likely to appear. As zackattack points out, for example, the decimal expansion of 1/9 does not appear in the digits of pi.