Re: Pi

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Re: Pi

Could you post the highest actual decimal that you know? I'm making a
program and want the actual number so I can compare.

Colin Guillas wrote in message <350C9436.5177@nrcan.gc.ca>...
>There is another way to find PI, and it can be implemented in TI Basic,
>(Or any other language).  I do it on computers that don't spit at me
>after the 8th decimal place... scientific notation really bugs me. :-)
>Anyway, using a loop, this is PI:
>
>PI=4(1-1/3+1/5-1/7+1/9-1/11...)
>If you represent the fractions as 1/a and keep adding two to a, you can
>keep a running total.
>There are workarounds on 386 and 486 processors using QuickBasic that
>allow you to calculate to 127 (or so) decimal places.  If you run the
>program and leave the computer for the appropriate numbers of
>minutes/hours, you'll comeback to the right value, if you double check
>it.
>BTW, I have Carl Sagan and his book 'Contact' to thank for this...
>although I can't find the ones and zeroes in his later chapters. :-)
>
>
>Bart Haagdorens wrote:
>>
>> Rhombus wrote:
>>
>> > One simple explanation is :
>> >
>> > PI is the circumference of a circle divided by its diameter.
>> > But the circumference cannot be measured or calculated exactly.
>> > Mathematicians get an approximation of this circumference, and hence of
PI,
>> > by calculating the circumference of a regular polygone with, say 1000
sides.
>> > This can be done exactly with a little trigonometry.
>>
>> There is another way, using the Talor Polynominal of atan(1).
Theoretically,
>> atan(1)=pi/4, so if you could get a good approximation of atan(1), and
then
>> multiply it by 4, you'd also find pi.
>> With the Taylor Polynominal of atan(x)=x - x^3/3 + x^5/5 -x^7/7 + x^9/9 +
...
>> you could calculate pi/4 as accurate as you'd want, simply by taking some
more
>> terms into the sum.
>>
>> People who own a TI-92, can easily calculate pi theirselves (I don't know
wether
>> it's possible with other TI's, it depends on wether they can calculate
the
>> Taylor-polynominal. You could ofcourse enter the polynominal by hand...)
>>
>> First you calculate the Taylor polynominal upto let's say the 21st grade.
>>
>>     taylor(tan-1(x),x,21)
>>
>> Then you calculate it for x=1 (using WITH for example). You multiply it
by 4,
>> and there's your own approximation of pi!
>>
>>    (in this case, it would be 11757173 / 14549535 * 4 = 3.23232)
>>
>> That's not very close, but the approximation becomes better by taking
more and
>> more terms...
>>
>>   (up to the 49th term, the result would be 3.18158, that's a little
better)
>>
>> Perhaps this is not the easiest way to calculate pi, but it's certainly a
>> reliable one!
>>
>> Within Taylor's theory, it's even possible to calculate how big the
deviation in
>> your result versus the exact value can be, but that's something for your
math's
>> teacher!
>
>--
>Colin Guillas       Ringmaster For Commodore Ring
>http://cbmring.home.ml.org  ringmaster@ottawa.com
>Kinetix Web Design     http://kinetix.home.ml.org
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