*To*: mathgroup@smc.vnet.net*Subject*: [mg11950] Re: [mg11915] how to compute pi by using continued fraction?*From*: Levasseur <levasseu@bit-net.com>*Date*: Fri, 10 Apr 1998 01:03:40 -0400*References*: <199804090433.AAA22105@smc.vnet.net.>

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 compute the representation to many terms. Ken Levasseur UMass Lowell

**References**:**how to compute pi by using continued fraction?***From:*"Jing S Chen" <jchen06@rocketmail.com>