1 2 Previous Next 24 Replies Latest reply: Oct 16, 2007 2:09 AM by 800282 Go to original post
• ###### 15. Re: Calculating Pi
As far as I know there are very few series that converge more slowly to pi than that one.
It would be pretty hard to converge more slowly, given that the term ratio tends to unity.
• ###### 16. Re: Calculating Pi
A very fast approximation of by was invented by Machin --
``pi/4= 4*atan(1/5)-atan(1/239)``
where the Taylor expansion of the arctangent function is used.

Nice little anecdote: in a Dutch Bible in the book of Kings, pi is approximated as "the circumference
equals three times the diameter of a circle". That's written in verse 22:7

kind regards,

Jos
• ###### 17. Re: Calculating Pi
A very fast approximation of by was invented by Machin
"of by was"? What nonsense is that? What moron wrote this? I certainly didn't; 't must've been some
glitch in my broadband connection or something ... or a temporary insanity of a keyboard ... but not me.
• ###### 18. Re: Calculating Pi
pi/4= 4*atan(1/5)-atan(1/239)
That's usable, but not "very fast" unless by comparison with atan(1).
• ###### 19. Re: Calculating Pi

<Homer accent>

Mmmmmm.... pie....

</Homer accent>
• ###### 20. Re: Calculating Pi
pi/4= 4*atan(1/5)-atan(1/239)
That's usable, but not "very fast" unless by comparison with atan(1).
True, I shouldn't have said "very" fast. Here's a nice link from the MathPages, elaborating a bit
on this arctangent Taylor expansion stuff -- http://www.mathpages.com/home/kmath373.htm

kind regards,

Jos
• ###### 21. Re: Calculating Pi
Hi, umm... I have to do the same assignment for my programming class,

but i have only learned the basic things of java (standalone, loops, selection, etc <but not too much>)

and i am expected to do a program like this,

so is there a MUCH easier way of doing this program

with only loops and simple stuff like that?
• ###### 22. Re: Calculating Pi
so is there a MUCH easier way of doing this program

with only loops and simple stuff like that?
The code samples provided so far are about as simple as it comes, and they only use "loops and simple stuff like that."
• ###### 23. Re: Calculating Pi
I am having trouble doing this with a university prac....

Pi= 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ..

Can anyone help out please, i'm not very good at Java....
• ###### 24. Re: Calculating Pi
nick_8188 wrote:
I am having trouble doing this with a university prac....

Pi= 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ..

Can anyone help out please, i'm not very good at Java....
\\
No time to waist then:
http://java.sun.com/docs/books/tutorial/getStarted/index.html
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