So that's kind of interesting. If you start with any English phrase, or any piece of literature for that matter, and repeatedly write the number of letters in the phrase in English, you end up at "four". I wonder what the smallest lengths of text are that survive n iterations... ----- Original Message ----- From: "Gareth McCaughan" <gareth.mccaughan@pobox.com> To: <math-fun@mailman.xmission.com> Cc: "Eric Angelini" <Eric.Angelini@kntv.be> Sent: Tuesday, September 05, 2006 12:29 PM Subject: Re: [math-fun] Lost in fraction
This fraction has a nice self-referential smell (in french) : ... ... take any digit of (a); when written in french, this digit has as much letters as described by the next digit : ... What could be a similar english fraction ?
The English-language number -> length mapping has a unique fixed point, where all iterations end up. So we'd get, e.g., 1354444444444. Put the decimal point at a place of your choosing and follow the same procedure as before; so, e.g.,
x = 1.35444444444... 10x = 13.54444444444... 9x = 12.19000000000... = 1219/100
so x = 1219/900.
-- g
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