More slices of PI

/*
Area under curves and analysis of dimensionality
Defining PI in a new way.
It reaches M_PI to 7 digits at 10^8 samples

Doing Pi
   Add sqrt(1-x^2) from 0 to 1 divide by steps

Doing volume of a sphere also
*/
/**
@name="MakingPI"
@version="2"
@author="moteyalpha"
*/
#include <stdio.h>
#include <math.h>
int main(int argc, char *argv[])
{
double s,s2,stepsize,MyPi,d;
int i,i2;
int steps;
double fsteps=10000000.0;
steps=10000000;
stepsize=1/(fsteps);

/* The area without PI */
MyPi=0.0;
for (i=1;i<steps;i++)
 {
 s = sqrt(1-(stepsize*i)*(stepsize*i));
 MyPi=MyPi+s;
 }
d=MyPi/fsteps;
printf ("My PI=%f .. M_PI=%f\n",4*d,M_PI);

/* Now the cubic without PI */
fsteps=60000.0; /* about two minutes */
steps=(int)fsteps;
stepsize=1/(fsteps);
MyPi=0.0;
for (i=1;i<steps;i++)
 {
 s = sqrt(1-(stepsize*i)*(stepsize*i));MyPi=MyPi+s;
 for (i2=2;i2<steps;i2++)
  {
/* Avoid that nasty imaginary number */
  if ((s*s-(stepsize*i2*s)*(stepsize*i2*s))>0.0)
   {
   s2 = sqrt(s*s-(stepsize*i2*s)*(stepsize*i2*s));
   MyPi=MyPi+s2*s;
   }
  }
 }
d=MyPi/(fsteps*fsteps);
printf ("My sphere volume factor*3 is %f.\n",3*(8*d)/M_PI);
return 0;
}

Archimedes would have done it this way.

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