Calkin-Wilf-Newman function or something

[1MileCrash]

Calkin-Wilf-Newman function... or something

Homework Statement

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

Homework Equations

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.

 

[shaon0]

Homework Statement

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

Homework Equations

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.

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.

 

[calkin]

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).

 

[Redbelly98]

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...".

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.

You have found that B = π-3, which is an exact number. So what is 1-B here?