Approximating Pi with Polygons

I wrote a program that approximates Pi by using polygons. I used the formulars in the picture beyond.
In my code they are called innerPoly (\$c_{2n}\$) and outerPoly (\$C_{2n}\$).

And since you can calculate the circumference of a 2n-polygon with knowing the circumference of a n-polygon you will get the circumferences \$C_8\$, \$C_{16}\$, \$C_{32}\$ etc., knowing \$C_4\$.

$$
\begin{array}{l}
c_{2n} =& 2 \sqrt{2n^2-n\sqrt{(2n)^2-c_n^2}} \qquad&\textrm{for the inner polygon, with}\ c_4=4\sqrt{2} \\
C_{2n} =& \frac{4 n C_n}{2n + \sqrt{(2n)^2 + C_n^2}} &\textrm{for the outer polygon, with}\ C_4=8
\end{array}
$$

My thoughts are:

-
Would it make it anyhow better when I have a function called void PiApproximation() that writes my values to stdout already? I mean technically you can always put your full code into the main()-function, but when you have to use the same code-parts over and over again you should make a own function of it and call it, when u need it.
So I guess in this case it will make no difference if I use an own function or calculate the circumferences and print it in the main-function.

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What else can I improve?

pi_approx.c

```
#include
#include

#define INNER_FOUR 4*sqrt(2); //circumference c_4 of the inner tetragon(square)
#define OUTER_FOUR 8 //circumference C_4 of the outer tetragon

int power(int n, int p);

int main(void)
{
int n = 4;
double innerPoly = INNER_FOUR;
double outerPoly = OUTER_FOUR;

printf("PI-APPROXIMATION USING POLYGONS\n");
printf("===============================\n\n");
printf(" n I c_n/2 I C_n/2 I\n");
printf("---------I-----------------I-----------------I\n");

for (int i=3; n<=8192; n=power(i,2), i++)
{
printf(" %4d I %1.8lf I %1.8lf I\n", n, innerPoly / 2, outerPoly / 2);

innerPoly = 2 sqrt(2 nn - nsqrt(4 nn - innerPoly*innerPoly)); //formular c_2n
outerPoly = (4 n outerPoly) / (2 n + sqrt(4 nn + outerPolyouterPoly)); //

-
You asked,


Would it make it better if I had a function called PiApproximation?

The code in main does just one thing so it would not be an improvement to introduce a new function like this — the question would then be, what's the point of main?

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There is a dependency between the initial value of n and the initial values of innerPoly and outerPoly. It would make sense to put all the initialization code together.

-
Because n can never be negative it could be unsigned.

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The loop:

for (int i=3; n<=8192; n=power(i,2), i++)

is quite hard to follow because the loop variable is i but the termination condition is on a different variable n. Because the loop variable i is not used, it would be easier to follow the logic if you wrote:

for (; n <= 8192; n *= 2)

(This also avoids the need for the power function.)

-
The l modifier has no effect on the printf format specifier %f, and so should be omitted.

StackExchange Code Review Q#160846, answer score: 4