hyperlexian wrote:
moved from Random Discussion to Computers, Math, Science, and Technology
i have a question. when the digits of Pi are memorised, is a person just memorising one numerical representation of Pi? i always wondered about that - i think i remember hearing once that every representation we can make is just an estimate.
yes it would be a numerical representation. i cant really think of another way to represent it, other than the definition of what pi is. With rare exceptions i have only known of people memorizing pi represented in the decimal system (base ten positional notation). well i have only known of it being done in this way but any number can be represented in a different numeral system, so i'm sure there is someone out there who is memorizing it a different way.
it would be true that any representation would not be exactly pi, as it has been proven to be transcendental number. In any base in which it is represented the digits will continue infinitely, no rational pattern will at any point constitute any sort of end to its definition. But also keep in mind, in defining pi to these extents we are delving into an incomprehensibly infinitesimally small and shrinking ratio. There is really no practical application for knowing more than a few digits. Let us contemplate : 3.141 at this point every digit following is a fraction of .001; 3.141592 : .00059 could be considered significant, in that they could warrant the rounding of 3.141 to 3.142. but once you get to 3.141592, all digits following are just a portion of .000002. Of coarse as you continue down the digits become ten times less significant with each step.
heres some neat information i found on :
http://www.math.com/tables/constants/pi.htmMillions of digits have been calculated, with the record held (as of September 1999) by a supercomputer at the University of Tokyo that calculated 206,158,430,000 digits
Approximation of PiArchimedes calculated that Pi was between 3 10/71 and 3 1/7 (also written 223/71 < < 22/7 ). 22/7 is still a good approximation. 355/113 is a better one.
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dont know if that record is still unbroken 13 years later. this is just the first hit i came across as to how many digits of pi are presently known. 200 billion should be plenty, lol.
thank you for explaining that!! !! my brain couldn't quite "get" it, but i think that now i understand.