# 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

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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? – Dac Saunders 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