# Thread: Numbers e and pi

1. ## Numbers e and pi

I found the following 2 questions regarding e and pi in the special topics of my precalculus math book.

(1) e^(pi) + pi^(e) =

(2) e^(pi)^(e) + pi^(e)^(pi) =

2. Originally Posted by sologuitar
I found the following 2 questions regarding e and pi in the special topics of my precalculus math book.

(1) e^(pi) + pi^(e) =

(2) e^(pi)^(e) + pi^(e)^(pi) =

3. What's so special about those results ? I typed into google and it doesn't show anything particular ...
Or are you supposed to calculate it without a calculator ? Or simplify it ?

4. There is nothing special about them. I suspect that they are just exercises in using your calculator. Probably your calculator has a "$\pi$" key. If not, you can always use $\pi= 4tan^{-1}(1)$ (with your calculator in radian mode, of course). For "e" use either the " $e^x$ key to find $e= e^1$ or use the "inverse" "ln" keys.

5. I suspect that they are just exercises in using your calculator.
In the special topics of a precalculus maths book ?

6. ## Yeah...

I don't why this is called "special topics" by the author.
Now, can this be done without a calculator?

7. Originally Posted by sologuitar
I don't why this is called "special topics" by the author.
Now, can this be done without a calculator?

No, unless have have an integrated floating point unit processor in your cerebral cortex. And even with infinite processing power, you would not be able to get the exact answer, since $\pi$ and $e$ are irrationnal. Thus, you must use a calculator to get the best "approached" value.