OpenEuphoria

Re: Still is maybe offtopic maybe definitely

• Posted by Kat <gertie at PELL.NET> Feb 24, 2001
• 351 views

On 24 Feb 2001, at 17:00, andy_cranston at LWSYS.FSNET.CO.UK wrote:

> Got to chip in here :-]
> 
> It's a late follow up but I've just finished watching a videoed episode of
> "The Wonder Years" (Kevin Arnold etc.).  Ok it's not necessary to know the
> series or whatever but it had this way laid back math teacher that got me
> thinking.
> 
> Back to the thread... (I do ramble 
> 
> Ok *decimal* fractional numbers are difficult to represent in binary two's
> complement (integer and mantissia?) with anywhere near 100% accuracy.  0.25
> is fine but a third is no go.
> 
> Now PI *can't* be represented in a finite series of decimal (base 10)
> numbers.  I suspect that it *can't* be represented in a finite series of
> binary (base 2) numbers either.  My theorem:
> 
>     Can PI be presented in a finite series of fixed
>     limit based integers?
> 
> As an example can PI be represented in base 36 where 0 is 0, 9 is 9, A is
> 10, b is 11, Y is 35 and Z is 36?

I expect pi can be represented properly only in bases of integrals of 7, such as
base7,
base14, base21, etc., but i am not a mathemetician.

Kat


> Don't limit your self to small base numbering systems.  Base a million and
> one is perfectly fine in math (or as high as you need to go!).
> 
> As with all my ideas I'm sure there must be stuff out there that already
> covers or has covered it.  Links to it would be most welcome.
> 
> Regards,
> 
> Andy Cranston.
> 
> At 02:07 23/02/01 -0800, you wrote:
> >aku at inbox.as wrote:
> >> 
> >> In Windows calculator (calc.exe), (scientific mode)
> >> if we click on "pi" the display is: 3.1415926535897932384626433832795
> >> Then click "-", and select Edit/Copy. then select Edit/Paste.
> >> 
> >> So 3.1415926535897932384626433832795 subtract
> >> 3.141592653589793238462643383279 (no "5" in the display).
> >> 
> >> then click "=".
> >> 
> >> I get the result is 5.0288419716939931148196659300057e-31
> >> 
> >> and so on ...
> >
> >The correct answer up to 10e-62 is:
> >5.0288419716939937510582097494459e-31
> >in comparison to your result:
> >5.0288419716939931148196659300057e-31
> >
> >See the difference?! So far to accuracy.
> >
> >Have a nice day, Rolf 
> >
> >PS: 
> >
> >If you want to find it out yourself, here is PI up to about 1000 decimal
> >digits. You can never represent the true value of PI by decimal
> >numbers!  
> >
> >Here are the first 1000 digits of PI in decimal representation (but what
> >for?): 
> >         
> >3.1415926535897932384626433832795028841971693993751058209749445923078164062
> 8620899862803482534211706798214808651328230664709384460955058223172535940812
> 8481117450284102701938521105559644622948954930381964428810975665933446128475
> 6482337867831652712019091456485669234590992071188568065167451942528543409596
> 2798591882336709925370852221809922606102035122988587416293486899692543597596
> 2450168323935335535189585278242475806800785024813944022838811069208716087268
> 2002093457201896863693165837580982216278044554224438736310551529920496341582
> 5560520531202114982360941059391159284170454059954772885655742682626925733132
> 5038462312209163710318948011942420558886250096137216524583613964673822832849
> 5353339759583290226779418162968167737618541879490468096290608719531536768829
> 4888131307168096117428255223625251333953006402282478948639832100317465189169
> 4369279502585139805382507188845356223535043232204643938233054624385621481085
> 2383769717133197158721033723844806221439090739290399585419356859519501823320
> 5903595386938
> >
> >
> >
> >
> 
> 
>