*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>