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Calkin-Wilf-Newman function or something

  1. Nov 4, 2011 #1
    Calkin-Wilf-Newman function.... or something

    1. The problem statement, all variables and given/known data
    I have no idea what this has to do with our current chapter in Calc II but it seems simple enough.

    [PLAIN]http://img253.imageshack.us/img253/2192/mathv.png [Broken]


    2. Relevant equations



    3. The attempt at a solution

    I managed fine for the first two, but I have no idea what to do for pi. The only way I can think to express pi as a rational plus a number is 3 + (pi - 3). Evaluating their function for that A and B can't give me an "exact answer" which is what they ask for.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 5, 2011 #2
    Re: Calkin-Wilf-Newman function.... or something

    f(x)=floor(x)+(1-[x-floor(x)])
    After, this change pi into it's series form to get infinite rational expressions although i'm not 100% sure if a change is required.
     
    Last edited by a moderator: May 5, 2017
  4. Nov 6, 2011 #3
    Re: Calkin-Wilf-Newman function.... or something

    You don't need the series form for pi.
    I'll show you how to do it for e = 2.7818... and you can see for yourself how
    to do it for pi.
    The integer part of e is 2, so here A=2, B=e-2.
    Thus f(e) = A + (1-B) = 2 + (1-(e-2)) = 5-e=2.21...
    (and yes, I'm the Calkin in Calkin-Wilf-Newman).
     
  5. Nov 7, 2011 #4

    Redbelly98

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    Re: Calkin-Wilf-Newman function.... or something

    calkin, welcome to PF.

    I think people may be overcomplicating this problem. By "exact number", I think the professor just wants students to write π as π, not as "approx. 3.1415" or "3.1415...".
    You have found that B = π-3, which is an exact number. So what is 1-B here?
     
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