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### Program to Calculate Pi

Date: 05/23/97 at 01:57:47
From: Toby Kirklin
Subject: The Formula for Pi

I am trying to write a program on my TI-83 calculator that would
calculate the infinite digits of Pi, while displaying them on-screen.
But I need to know the formula to calculate these digits. Would you or
any of your colleagues happen to know this?

Toby Kirklin

Date: 05/23/97 at 14:20:39
From: Doctor Spunk
Subject: Re: The Formula for Pi

Toby,

Because pi is irrational, you will never actually get very far in
calculating it with a TI-83. The machines that they use are huge
supercomputers.

One formula that has been proven is this:

oo
-----
\        6
)      ---  =   (pi)^2.
/       n^2
------

n= 1

By running a loop program on the calculator, you will see that this
does actually converge to Pi^2. So, instead of displaying the values
calculated, take the square root of the number that you have right
before it is displayed.

One word of caution! I do not have a TI 83, I am using an 82. I assume
that they are similar in a few ways. If you know that what I am
telling you will not work on an 83, try to find someone who knows.

It might look something like this.

1 stored as X.    0 stored as C.      Label 1.       6/x^2 stored as B

B+C stored as C.  Display (root C).   X+1 stored as X.     Goto 1.

Unfortunately this converges very slowly. Even after 1000 iterations,
it only has the number 3.14 in place.   However, if you have enough
patience, it will come out to pi.

Another way to calculate pi is the following.

2 x 4 x 4 x 6 x 6 x 8 x 8 x 10 x 10 x 12 x 12  .....    pi
------------------------------------------------        --
3 x 3 x 5 x 7 x 7 x 9 x 9 x 11 x 11 x 13 x 13  ......    4

Writing a program for this was a bit confusing.

(>> equals stored as)

2>>x.    3>>c.   1>>a.    Label 1.    x/c >>d.   d*a >>a.   Display 4a

x-c >>e   if e = -1. then    goto 2.    Else goto 3.  End.

Label 3.  c+2 >>c.  Goto 1.

Label 2.  x+2 >>x.  Goto 1.

This converges to pi. It takes a while also, but just think -- all
those mathematicians over the years never saw what pi was equal to!

There are other formulas, some of which use inverse tangents and other
weird ways of calculations. There are also plenty of Web pages on the
internet that are especially devoted to pi.  Check the bottom of our

http://mathforum.org/dr.math/faq/

pi, and the number of digits known so far.

-Doctor Spunk,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

Associated Topics:
High School Calculators, Computers
High School Sequences, Series

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