Find your birthday (or any other number) in pi ...
angio.net
angio.net
It is conjectured that pi is "normal" in the sense that the digits occur with equal liklihood. Making that statement precise is exceedingly hard, and not very enlightening.
EDIT: philh points out that the full definition of "normal" says that every block occurs equally often (a concept that needs care to make formally correct) and that does imply that every finite sequence does occur.
pi is known to be transcendental. It is not only not rational (cannot be expressed as the ratio or integers (although 355/113 is close and you can get as close as you like by using bigger numbers)) but it is also not the root of any polynomial with integer coefficients (rationals being a special case).
The digits of pi cannot become periodic.
None of the above is enough to show that every finite number occurs "eventually". As an example, consider the number:
0.123 112233 111222333 111122223333 111112222233333 ...
Here the digits 1 through 3 occur equally often, it never becomes periodic, it is transcendental, and yet the sequence 321 will never occur. Now instead of using 1 through 3, generalise to using 1 through 9.
It is generally believed that the digits are "effectively random" which means any finite sequence will occur with probability 1, but the observations made above are not enough to ensure that. (EDIT: although the full definition of "normal" does, rather thanthe limited version I originally put - thanks to philh for the correction).
(edited a typo 133 -> 113 : thank you for the correction)
That's only part of it. You need that every block occurs as often as every other block of equal length. So every digit occurs as often as every other digit; every pair of digits occurs as often as every other pair; every triple occurs as often as every other triple; and so on. So the number you give is not normal in base 3.
A consequence of normality is that every finite sequence of digits eventually appears.
355/113
Be warned that 50 million digits of pi takes up 50 megabytes. This can take up to 4 hours to download with a 28.8k modem!
"The string 03161953 occurs at position 30,263,003 counting from the first digit after the decimal point."
But if I search for that result, it doesn't find it.
If I search for 12345678 it finds it and you can see 89 before it. Why can't I search for that number?
Maybe I'm getting the math wrong though?
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?
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.
This is what I remember, but I could be wrong.
Why am I not surprised? :)
I'm so sad.
:)
Who can get closest to zero?
Wikipedia lists Khaled, Algerian raï musician; Richard Ramirez, American serial killer; Tony Robbins, American motivational speaker as being born on 29 February 1960.
Oddly searching for 29021960 doesn't return a result. But searching for 2902196 does and shows there's a zero after it.
3-11-82