What has been the most decimal places for the calculation of Pi?
And more importantly, why did they waste time doing it????
- 1 decade agoFavorite Answer
While the value of pi has been computed to more than a trillion (10^12) digits, elementary applications, such as calculating the circumference of a circle, will rarely require more than a dozen decimal places
In 1999 Yasumasa Kanada calculated 206,158,430,000 decimal digits of Pi, setting a world record, only to top it himself three years later.
In 2002 his team at the University of Tokyo calculated 1,241,100,000,000 digits. This calculation took more than 602 hours on a Hitachi SR8000 computer and required more than 1 terabyte of memory (duh!). The results were used to calculate the frequency of all ten digits in Pi and they all are quite close to 10%. Of course, this is not enough to prove that the Pi is normal (that is that every sequence of numbers of certain length has the same probability of appearing in Pi).
But another approach is likely to prove more fruitful.
In 1995 David Bailey, Peter Borwein, and Simon Plouffe made an exciting discovery. They found a simple formula for calculation of Pi that incidentally allowed independent calculation of any single hexadecimal digit of Pi. This formula (named BBP formula after the scientists who discovered it) is provided below:
Pi = SUMk=0 to infinity 16-k [ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ]
This formula still doesn't prove that Pi is normal, but it now links the distribution of digits in Pi to the field of chaotic dynamics. There is an unproved but plausible conjecture that certain sequences (just like the one described by the above formula) "uniformly dance in the limit between 0 and 1". This explains why the digits in Pi (and other constants, like log(2) or square root of 2) appear to be random, but doesn't prove that they actually are. However, if it is proved, the normality (in base 2) of Pi and many other mathematical constants will follow.
WHY WOULD SOMEONE GO THROUGH THE TROUBLE?
Well, first if you could convince someone to let this be your job, you would never go without a job. Its kind of like trying to find all the prime numbers.
My senior seminar project was on infinity. We worked a lot with numbers such as pi, primes, etc. You'd be happy to know that most of the big infinity people (such as Cantor) were driven to maddness and by the end of the class I felt as if I were going mad!
- Anonymous1 decade ago
How i wish i could calculate pie
3 . 1 4 1 5 9 3
- 4 years ago
i thought pi still wasnt calculated
- Lonnie PLv 71 decade ago
I don't remember the exact number but it was several thousand places done by a man in Japan.
Why? Kind of like climbing Mt. Everest -- because it's there!
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- webcop33Lv 41 decade ago
One day someone might find a pattern that's why. It may be like a set of 239827489237210893712 numbers repeated over and over.
- 1 decade ago
"Life is not fair - engoy it!"