Program to Calculate PiDate: 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? Thank you for your time, 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 "Pi" page (look in the table of contents of the Dr. Math FAQ): http://mathforum.org/dr.math/faq/ You'll also find links there to questions about the irrationality of pi, and the number of digits known so far. -Doctor Spunk, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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