X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,43829188203eedab X-Google-Attributes: gidf996b,public X-Google-ArrivalTime: 2001-08-23 20:50:09 PST Path: archiver1.google.com!newsfeed.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!feed2.news.rcn.net!rcn!news.voicenet.com!news-out.spamkiller.net!propagator-la!news-in.superfeed.net!newsfeed01.tsnz.net!canterbury.ac.nz!mathwft From: mathwft@math.canterbury.ac.nz (Bill Taylor) Newsgroups: alt.ascii-art Subject: Re: mathematical expressions Date: 24 Aug 2001 03:48:19 GMT Organization: Department of Mathematics and Statistics, University of Canterbury, Christchurch, NewZealand Lines: 46 Message-ID: <9m4iq3$p1s$3@cantuc.canterbury.ac.nz> References: <3B80D892.C7B984F9@rz.uni-karlsruhe.de> <9lsjqs$4in$1@cantuc.canterbury.ac.nz> <3B82119F.1AB52C53@rz.uni-karlsruhe.de> <9ltdks$cs7$1@cantuc.canterbury.ac.nz> <9lv7lr$18d$1@cantuc.canterbury.ac.nz> <9m3tk1$8g26$1@ID-39741.news.dfncis.de> NNTP-Posting-Host: e220-0.math.canterbury.ac.nz X-Newsreader: xrn 8.02 Xref: archiver1.google.com alt.ascii-art:7118 Michael Schierl writes: |> >|> > .----------------------------------------------------------- |> >|> > / .------------------------------------------------ |> >|> > / / .------------------------------------- |> >|> > / / / .-------------------------- |> >|> > / / / / .--------------- |> >|> > / 1 + 1 / 1 + 2 / 1 + 3 / 1 + 4 / 1 + 5 /~~~... |> >|> > v v v v v v |> >|> |> >|> |> > they are all square roots. |> i would say gur erfhyg vf rknpgyl gjb. (ROT13) You are correct! Here is your chocolate candy... ____ ___ .' /:::. ___ \ "-. / (:::-'\ .-" / > -=.\/:\__\/__ \/.=- < > -='/\::::/\:::\/\'=- < /__.-' \::' )::/ '-.__\ '.__/::' |> it is simple to determine this by a small program Yes, you can do that; though some of us might say that's a little bit cheating. Of course, once one guesses the answer, it's not too hard to prove, (say using induction). The fascinating thing about these infinitely nested square roots is how incredibly rapidly the numbers inside can increase, yet still have the whole thing converge. Much more than infinite series and products and things. The numbers can be as high as c^(2^n) or so. Very unusual in math. Also interesting is that the "2" there cannot be increased, though the constant "c" can be anything. Weird huh!? ----------------------------------------------------------------------------- Bill Taylor W.Taylor@math.canterbury.ac.nz ----------------------------------------------------------------------------- And Abraham looked upon the Lord and said: "We are your chosen people, and you want us to cut off the tips of our WHAT?!" -----------------------------------------------------------------------------