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reading digits of irrational numbers

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This question hasn''t got a lot to do with gaming, but would rather be handy for math software and such, and MAYBE also to generate a fractal world for a game I''m planning to make. My question is: is it possible to know a certain digit of an irrational number without knowing the previous ones. For example, is it possible to know the 500th digit (base 10) of Pi without having to know all the 499 previous ones? Or the 500th digit of ln((1*6/8*7+63-5)^1.326)? And if so... how?

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For Pi, at least, there is a way to get arbitrary hex digits. (Good luck with the Fortran code).

Beware that algebraic (i.e. non-transcendental) irrational numbers repeat themselves with some finite period.

STFW for any 'Pi' page and you'll find googolplexes of methods and theories.

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[edited by - Fruny on June 30, 2002 7:44:12 PM]

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Search for type in "Bailey Pi" at google and look for what turns up, it is stuff about that Pi formula but in a non language specific form (I think it is Bailey-Boffin, but I''m not sure how to spell the Boffin, leaving it out will get the results)

The equation itself is quite simple, just 4 or so terms.

What you must remember is that 1) it is hex and 2) just because it doesn''t repeat itself, doesn''t mean the distribution of numbers is random.

Trying is the first step towards failure.

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