﻿ C program for the plane area of an egg shaped curve
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// Calculation Program for the plane area of an egg shaped curve, 08 (Tues.) Dec., 2009

// egg equation: (x*x+y*y)**2=a*(x**3)+(a-b)*x*(y**2), The case that a=4 and b=3.2 (or, a=1 and b=0.8) may be the nearest shape to an actual egg.
// The general condition needs b<=a, and in the case of b=0, the curve is led to a circle.

// file name: area.c

#include< stdio.h>
#include< math.h>

void main(void)
{
double a,b,x,y,dx,xmax,area,darea,pi;

for(;;)
{
printf("Input of constant a; a= ? ");
scanf("%lf",&a);
if(a>0)
{
break;
}
else
{
printf("Please input the value of a after correcting a as a>0.\n");
}
}
for(;;)
{
printf("Input of constant b; b= ? ");
scanf("%lf",&b);
if(b>=0&&b<=a)
{
break;
}
else
{
printf("Pleease input the value of b after correcting b as 0< b < a or b=0 or b=a.\n");
}
}

printf("\n");

pi=3.1415927;

xmax=a;// the maximum value of x
dx=xmax/100000;

// execution of calculation
if(b==0)
{
area=pi*a*a/4;
}
else
{
for(x=0;x<=xmax;x=x+dx)
{
y=sqrt(((a-b-2*x)+sqrt(4*b*x+(a-b)*(a-b)))*x/2);
darea=y*dx;
area=area+darea;
}
area=2.0*area;
}

printf("The plane area of the egg shaped curve; A=%lf\n",area);
printf("\n");

printf("end\n");
}// the end of the program

```

RETURN