Question

Please see the formulæ below.

It’s the solution to a circle chord problem where A is the arc length and C is the chord length.
I want to find the Radius r.

The formula below uses factorials and powers etc which I don’t know how to express in Objective C.

Can somebody help by converting the formula into Objective C language?

a = A² – C²
b = -2A^4/4!
c = 2A^6/6!
d = -2A^8/8!

//Let:
f = c/a-b²/3a²

g = d/a+2b³/27a³-bc/3a²

x = cuberoot(-g/2 + sqrt(g²/4+f³/27)) – cuberoot(g/2 + sqrt(g²/4+f³/27)) - b/3a

r = sqrt(x)

Answer 1

This should work:

double factorial(int x)
{
    double result = 1;
    for (x = x; x > 0; x--)
    {
        result *= x;
    }
    return result;
}

…

int A = 20;
int C = 25;

double a = A*A - C*C;
double b = -2.0*pow(A, 4.0)/factorial(4);
double c = 2.0*pow(A, 6.0)/factorial(6);
double d = -2.0*pow(A, 8.0)/factorial(8);

//Let:
double f = c/a-(b*b)/(3.0*(a*a));

double g = d/a + 2.0*pow(b, 3.0)/(27.0*pow(a, 3.0))-(b*c)/(3.0*a*a);

double x = pow(-g/2.0 + sqrt(g*g/4.0+pow(f, 3.0)/27.0), 1.0/3.0) - pow(g/2.0 + sqrt(g*g/4.0+pow(f, 3.0)/27.0), 1.0/3.0) - b/(3.0*a);

double r = sqrt(x);