fafalone Posted February 4, 2003 Share Posted February 4, 2003 Using the Bailey-Borwein-Plouffe algorithm, it is possible to calculate any digit in the hexadecimal expansion of pi without calculating any of the preceeding digits. :pi: = :lsum: (4/(8n+1) - 2/(8n+4) - 1/(8n+5) - 1/(8n+6))*(1/16)n for n=0 to :inf: Is there ever a hope of formulating an equivalent in decimal form? What does this say about whether pi might have an ending? Link to comment Share on other sites More sharing options...
blike Posted February 4, 2003 Share Posted February 4, 2003 Who wants my elite VB program that utilizes this forumla. Its rather slow though. Link to comment Share on other sites More sharing options...
fafalone Posted February 4, 2003 Author Share Posted February 4, 2003 That and it's probably in base-10 rather than 6 Link to comment Share on other sites More sharing options...
blike Posted February 4, 2003 Share Posted February 4, 2003 Nah its in base-6. I've tested it out to 10,000 digits, matches up with what the formula should produce. Link to comment Share on other sites More sharing options...
JaKiri Posted February 4, 2003 Share Posted February 4, 2003 Originally posted by fafalone What does this say about whether pi might have an ending? It doesn't. It's formed from a Taylor series. Link to comment Share on other sites More sharing options...
NSX Posted February 10, 2003 Share Posted February 10, 2003 Originally posted by MrL_JaKiri It doesn't. It's formed from a Taylor series. which is... Link to comment Share on other sites More sharing options...
JaKiri Posted February 10, 2003 Share Posted February 10, 2003 Originally posted by NSX which is... The sum of an infinite number of ever expanding powers. Link to comment Share on other sites More sharing options...
NSX Posted February 10, 2003 Share Posted February 10, 2003 Originally posted by MrL_JaKiri The sum of an infinite number of ever expanding powers. Can you give me an example? Link to comment Share on other sites More sharing options...
the GardenGnome Posted February 22, 2003 Share Posted February 22, 2003 Is there ever a hope of formulating an equivalent in decimal form? What does this say about whether pi might have an ending? [/b] Pi is exactly 3! -Professor J. Frink Link to comment Share on other sites More sharing options...
fafalone Posted February 22, 2003 Author Share Posted February 22, 2003 Phi is (1+sqrt(5))/2 The Golden Ratio, :lcphi: Link to comment Share on other sites More sharing options...
Dave Posted March 1, 2003 Share Posted March 1, 2003 Originally posted by NSX Can you give me an example? he explained it in rather complex terminology basically, if you have a function like cos(x), e^x or any function that has continuous derivatives, you can expand it in terms of x. a really crude way to think of it is kind of like a more complicated binomial expansion. you start of by presuming that some function of x, f(x) = a + bx + cx^2 + dx^3 + ... where a, b, c, d etc are constants. for example, if you take f(x) = e^x, then you can say when x = 0, a = 1. then by differentiating it, you can see that b = 1, then again to see that c = 1/2 and d = 1/6, e = 1/24, etc so therefore e^x = 1 + x + x^2/2! + x^3/3! + ... + x^n/n! you can test it in your calculator if you want, but it works. btw, this is a bit overly simplified, i've not really studied these things in detail, but this is the basic principle behind it. Link to comment Share on other sites More sharing options...
fafalone Posted March 1, 2003 Author Share Posted March 1, 2003 Isn't a series like that a sum tho; this allowed for calculating any digit of pi without calculating any of the preceeding digits. Link to comment Share on other sites More sharing options...
JaKiri Posted March 8, 2003 Share Posted March 8, 2003 Originally posted by fafalone Isn't a series like that a sum tho; this allowed for calculating any digit of pi without calculating any of the preceeding digits. If you calculate any digit of pi without having to know its surroundings, you would have to calculate an infinite number of 0's before you could be sure that it terminated. Link to comment Share on other sites More sharing options...
the GardenGnome Posted March 8, 2003 Share Posted March 8, 2003 So far there has been something around 6.5 billion digits in pi. And it's still not exact. Link to comment Share on other sites More sharing options...
JaKiri Posted March 8, 2003 Share Posted March 8, 2003 Originally posted by the GardenGnome So far there has been something around 6.5 billion digits in pi. And it's still not exact. Of course it isn't It's a transcendetal number. It has been proven to be infinite. (but between the values of 3.1 and 3.2) Link to comment Share on other sites More sharing options...
zakfab Posted July 23, 2003 Share Posted July 23, 2003 More importantly, why does pi come up in all areas of science? Link to comment Share on other sites More sharing options...
Dave Posted July 23, 2003 Share Posted July 23, 2003 Nobody knows really - it's an extremely important constant, but it still surprises me when it turns up in a really obscure part of mathematics (like the infinite limits of sums going to things like pi^2/6). I suppose its because circles, angles, and more importantly radians are used in so many parts of science. Link to comment Share on other sites More sharing options...
NSX Posted July 24, 2003 Share Posted July 24, 2003 Originally posted by dave he explained it in rather complex terminology ... you can test it in your calculator if you want, but it works. btw, this is a bit overly simplified, i've not really studied these things in detail, but this is the basic principle behind it. Cool. Thanks. It took a few minutes, but it sunk in Link to comment Share on other sites More sharing options...
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