Re: how to compute pi by using continued fraction?
- To: mathgroup@smc.vnet.net
- Subject: [mg11979] Re: how to compute pi by using continued fraction?
- From: Craig P Earls <cearls@ix.netcom.com>
- Date: Fri, 17 Apr 1998 02:21:26 -0400
- Organization: Netcom
- References: <199804090433.AAA22105@smc.vnet.net.> <6gp1im$4p4$1@dragonfly.wolfram.com>
Levasseur <levasseu@bit-net.com> writes:
> Jing S Chen wrote:
> >
> > Hello:
> > I'm a student of City College of San Francisco. Right now, I have a
> > project that I've been working on at least 4 days. Yet I still have no
> > idea at all.
> > The purpose of the project is to compute pi by using continued
> > fraction. Here is the formula.
> >
> > pi = 3 + ( 1 / ( 7 + ( 1 / ( 7 + ( 1 / ( .... 1 / 7)
> >
> > that means
> > 1
> > pi = 3 + -----------
> > 7 + / 1 \
> > ( ------ )
> > \ 7 + /
> > .......
> > 1
> > + ----
> > 7
> >
> > Is here any one who has a program that can follow the above formula and
> > can generate pi?
> >
> > Jing S. Chen
> > e-mail: jchen06@hills.ccsf.cc.ca.us
>
> Jing:
>
> You are computing the continued fraction <3,7,7,7,...> which is NOT
> equal to Pi. If fact any cf that is periodic like has the form a + b
> Sqrt[c]. The continued fraction representation of pi is <3,7,15,1...>
> and has no pattern. The NumberTheory`ContinuedFraction.m package will
Here is a continued fraction definition of Pi attributed to Ramanujan
that definitely has a pattern:
Pi 1
-- = --------------
4 1 + 1
---------
3^2 <---The pattern is odd numbers
2+ --------
5^2
2+ -------
...
It takes quite a long time to converge. --
----------------------------------------------------------------------
Craig P Earls, LT U.S. Navy cearls@ix.netcom.com MIT Naval
Construction and Engineering cpearls@mit.edu
----------------------------------------------------------------------
- References:
- how to compute pi by using continued fraction?
- From: "Jing S Chen" <jchen06@rocketmail.com>
- how to compute pi by using continued fraction?