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Thread: Pi

  1. #1 Pi 
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    Hello Pi has intrigued me lately after watching the following clip: https://www.youtube.com/watch?v=X3AlKU7dfOM


    I believe that it would be very difficult to simply remember 20,000 digits but if there were any known exact circumference/diameter of a circle so I could just do long division in my head. Or a formula for finding digits I could just do the calculations in my head and go on forever.

    Is that possible? How do computers solve digits of Pi?


    I assume there is some sort of formula.


    Thank you!!!


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  3. #2  
    Forum Professor astromark's Avatar
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    ~ Throw the computer away... For the solving of Pi can be amusingly understandable just with a ball and some string..
    For almost all problems involving the number of times a diameter fits around the circumference of a circle, or was that the number of times a diameter can be divided into a circumference.. What volume of concrete is required for a circular slab of my Observatory..
    I do not require a computation of greater than two digits after the point.. # 3.14 is any place accurate enough. Looking for a termination of a infinite equation that is not available.. or required.. Mathematics for the sake of mathematics will undo your soul..
    ~ Medication will be required for the piece of mind of the quest is not attainable.


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  4. #3  
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    Quote Originally Posted by astromark View Post
    ~ Throw the computer away... For the solving of Pi can be amusingly understandable just with a ball and some string..
    For almost all problems involving the number of times a diameter fits around the circumference of a circle, or was that the number of times a diameter can be divided into a circumference.. What volume of concrete is required for a circular slab of my Observatory..
    I do not require a computation of greater than two digits after the point.. # 3.14 is any place accurate enough. Looking for a termination of a infinite equation that is not available.. or required.. Mathematics for the sake of mathematics will undo your soul..
    ~ Medication will be required for the piece of mind of the quest is not attainable.
    I see, yeah I wasn't planning on using this method to do calculations I just can do a lot of calculations in my head well so if I knew two exact values of circumference and diameter I could just use long division and after a couple hours recite a few thousand digits
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  5. #4  
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    Just for my own entertainment and those of others I guess, not for any scientific purpose of course
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    Forum Freshman pzkpfw's Avatar
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    Don't mind astromark, this is a common comment from him. He's perfectly correct that you usually don't need very many digits, but he seems to get irked about anyone wanting more digits (in anything) than he thinks are needed. (And I've seen him try to assert his irritation as being equivalent to a mathematical fact).

    You can find some interesting math by googling "calculate pi". e.g. see the Gregory-Leibniz series at 3 Ways to Calculate Pi - wikiHow
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    Quote Originally Posted by pzkpfw View Post
    Don't mind astromark, this is a common comment from him. He's perfectly correct that you usually don't need very many digits, but he seems to get irked about anyone wanting more digits (in anything) than he thinks are needed. (And I've seen him try to assert his irritation as being equivalent to a mathematical fact).

    You can find some interesting math by googling "calculate pi". e.g. see the Gregory-Leibniz series at 3 Ways to Calculate Pi - wikiHow
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  8. #7  
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    BTW, computers use a variety of different algorithms for generating the digits of pi. The two most interesting are the spigot algorithm and the Bailey-Borwein-Plouffe formula. The spigot algorithm does what it's name implies and just drips out the next digit each iteration. The BBP formula can give you any specific digit in base 16, so if you want the 1,000,001st digit, you can calculate that directly. Neither can be done in your head though, and I don't know of any algorithm for pi that could be.
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  9. #8  
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    Quote Originally Posted by ScienceNoob View Post
    I see, yeah I wasn't planning on using this method to do calculations I just can do a lot of calculations in my head well so if I knew two exact values of circumference and diameter I could just use long division and after a couple hours recite a few thousand digits
    The trouble with this is, to get 1,000 digits of pi you would need to memorise a pair of 1,000-digit numbers.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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  10. #9  
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    Quote Originally Posted by pzkpfw View Post
    Don't mind astromark, this is a common comment from him. He's perfectly correct that you usually don't need very many digits, but he seems to get irked about anyone wanting more digits (in anything) than he thinks are needed. (And I've seen him try to assert his irritation as being equivalent to a mathematical fact).

    You can find some interesting math by googling "calculate pi". e.g. see the Gregory-Leibniz series at 3 Ways to Calculate Pi - wikiHow
    WOW! Thank you! "Gregory-Leibniz series" seems to be a very useful one for this, but I wouldn't be able to recite Pi digit by digit so then that leads to the question how would the person in the video be able to recite so many digits? I find it unlikely that it is memory despite have an incredible memory ability at least 1 digit would be not remembered correctly?
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  11. #10  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by ScienceNoob View Post
    I see, yeah I wasn't planning on using this method to do calculations I just can do a lot of calculations in my head well so if I knew two exact values of circumference and diameter I could just use long division and after a couple hours recite a few thousand digits
    The trouble with this is, to get 1,000 digits of pi you would need to memorise a pair of 1,000-digit numbers.

    I see what you are saying,

    I wonder if there are two whole numbers that match up (circumference and diameter) then long division again would have a possibility.
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  12. #11  
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    Quote Originally Posted by MagiMaster View Post
    BTW, computers use a variety of different algorithms for generating the digits of pi. The two most interesting are the spigot algorithm and the Bailey-Borwein-Plouffe formula. The spigot algorithm does what it's name implies and just drips out the next digit each iteration. The BBP formula can give you any specific digit in base 16, so if you want the 1,000,001st digit, you can calculate that directly. Neither can be done in your head though, and I don't know of any algorithm for pi that could be.

    Both of those formulas are extremely useful! Although like you said it seems almost impossible that those could be done without a calculator, thank you for the share I appreciate it!
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  13. #12  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by ScienceNoob View Post
    I wonder if there are two whole numbers that match up (circumference and diameter) then long division again would have a possibility.
    Pi is irrational and so cannot be expressed as the ratio of two integers. Although, you can get as close as you want. For example 314/100 is a crude approximation and 314159/100000 is better. But you would still have to memorise 1,0000 digits to get pi to 1,000 digits!
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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  14. #13  
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    I see, yeah I wasn't planning on using this method to do calculations I just can do a lot of calculations in my head well so if I knew two exact values of circumference and diameter I could just use long division and after a couple hours recite a few thousand digits
    The point that people are trying to make is that pi is an irrational number. Therefore you cannot have two exact values.
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  15. #14  
    Forum Radioactive Isotope MagiMaster's Avatar
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    People who recite digits of pi do it as a feat of memory. As far as I know, none of them are doing any calculating.

    When you're calculating digits of pi, it's mainly a way of showing off how fast your computer is. (More or less. It can also be used as a stress test or rarely to demonstrate a new algorithm.)
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  16. #15  
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    Another way of memorizing pi is in binary, but memorizing the number of 1's and 0's that run in sequence, so

    11.0010010000111111...

    would be 2 (1's), point, 2 (0's), 1 (1), 2 (0's), 1 (1), 4 (0's), 6 (1's), etc or

    2.212146...

    If you want to give it a try, here's the first 100,000 binary digits of pi.

    At about the 84,560th digit there's a run of 16 zeroes, so you could just ignore the rest after that.

    Good luck.
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  17. #16  
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    Quote Originally Posted by jrmonroe View Post
    Another way of memorizing pi is in binary, but memorizing the number of 1's and 0's that run in sequence, so

    11.0010010000111111...

    would be 2 (1's), point, 2 (0's), 1 (1), 2 (0's), 1 (1), 4 (0's), 6 (1's), etc — or

    2.212146...

    If you want to give it a try, here's the first 100,000 binary digits of pi.

    At about the 84,560th digit there's a run of 16 zeroes, so you could just ignore the rest after that.

    Good luck.
    Wow people who have the ability to just remember 7 numbers in memory and not forget are able to count pi quite effectively

    I think that is what that man is able to do, he just tallies each of those numbers in his head while going along the list of binary in his head as well
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  18. #17  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Converting binary to decimal is much harder than just remembering the decimal digits.
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  19. #18  
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    Quote Originally Posted by MagiMaster View Post
    Converting binary to decimal is much harder than just remembering the decimal digits.
    Agreed. It might be easier for a while but eventually you'll have to remember so many digits of binary just for it to correspond to one number...the probability of just guessing a digit will be higher than guessing the binary and then converting...
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