# Are $e$ and $\pi$ dependent since $f(e)=\pi$ and$f(\pi)=e$?

It's stated that $\pi$ and $e$ are mathematical constants. But how can they be constants when there is a formula from one to the other, for instance Euler's formula. Since $e^{i \pi}=-1$ then is it true that we can express $e$ as a function of $\pi$ and vice versa? So if we can express $\pi$ in terms of $e$ then only one of these should be considered a mathematical constant since one in fact is a function of the other and therefore a dependence, not a linear dependence but clearly some formula.

There is a formula for the $n$-th digit of $\pi$, then should there also be a formula for the $n$-th digit of $e$? Why not?

Did I misunderstand what we mean when we say mathematical constant?

Thank you

-
Yes, you have misunderstood the meaning of the word constant. – Will Jagy Aug 16 '11 at 21:15
Thank you for letting me know. A similar example is Avogadro's number which sometimes is called a constant but in fact is a number and not a constant. How can I understand the difference between number and constant? I understand that something is not a constant when it is "at least one" or "at most one" etc trivial examples but maybe clarifying the difference i.e. Avogadro's number is not a constant could help me understand or good examples of what it and isn't a constant and whether the number of constants in mathematics is generally defined? – Nick Rosencrantz Aug 16 '11 at 21:25
A mathematical constant is a number with a standard, accepted definition with a unique, unchanging value - hence the word "constant." In English, constant does not mean independent, it means not changing. – anon Aug 16 '11 at 22:00

## 1 Answer

Mathematical constants are not like physical constants. In physics you try to reduce the amount of constants to a minimum, in mathematics constants are just values of major significance (check also this article). Of course for every two mathematical constants you can find a formula that relates the two constants, that doesn't mean you only need one of them.

-
Thank you for the info. I think I understand now that it's not like physics or chemistry where you try to agree upon constants and the number of constants. A mathematical constant could be something that just comes from a specific calculation and there could be infinitely many mathematical constants. So understanding the difference between physical constants and mathematical constants helps me clarify that my questions perhaps is more about mathematics and mathematical nomenclature rather than a mathematical question for some real mathematics. I'm glad to get this formalized. – Nick Rosencrantz Aug 16 '11 at 21:29
Good to hear that I could help :-) – Listing Aug 16 '11 at 21:30