# Pi Day MMXVII

2018-03-14, post № 192

**C**, **mathematics**, **programming**, #improper integral, #power series, #source layout, #Taylor series

Today it is the fourteenth of March 2018. Today’s date — when written in the M/D/Y format —, 3/14/18, looks close enough to Archimedes’ constant’s decimal representation for it to be the constant’s celebratory day.

As always on Pi Day, I have implemented an algorithm to generate 𝜋, albeit this year’s accuracy is not the greatest (Try it online^{ [1]}).

typedef double d;typedef long l;l f(l n ){l f=1;while(n>1)f*=n--;return f;}d ne(d v, l p){d r=1;for(l k=0;k<p;k++)r*=v;return r;}d ps(d(*c)(l),l i,d x){d s=0;for(l k=0;k<i;k++)s +=c(k)* ne(x, k);return s;} d exc ( l n){ return 1./f (n) ; } d exp(d x ) { return ps(exc ,20,x);} d G( d x){return exp(-x *x);}d I (d a,d b,d g,d (* f)(d )){d cs= 0;for( d x=a;x<= b;x +=g) cs+=f(x) *g;return cs ; } int main( ) { d pi_root =I( -2.5, 2.5 , 1e-4,G); d pi = pi_root * pi_root+(0xf&0xf0 ) ; printf( "%c%c%c%c%c%f%c" ,'p','i', ' ','=',' ',pi ,'\n' ) ; }

I use various methods of generating 𝜋 throughout the Pi Days; this time I chose to use an improper integral paired with a power series. 𝜋 is calculated using a famous identity involving infinite continuous sums, roots, e, statistics and — of course — 𝜋.

Furthermore, to compute 𝑒, the following identity is used.

Both formulae are combined, the approximated value of is squared and 𝜋 is printed to `stdout`

.

You can download this program’s prettified (some call it obfuscated, see above) source code pi.c and also the (nearly, as `#include`

is not missing so that the compiler does not need to guess my dependencies) equivalent code in a more traditional source layout tpi.c.

Happy Pi Day!

## Footnotes

- ▲ [2020-08-07] In the TIO link, there is some leading and trailing whitespace around the 𝜋.