How to approach pi in a circle

Question

I have received an admission assignment for the Computer Science program, where I have to approach PI. To calculate pi I have to make a ratio between the area of ​​a square, a circle, the total number of dots and the number of dots within the circle.

• N = total number of dots
• M = dots within the circle
• The diameter is 400

The formula of the area of ​​a circle

radius^2 * π or diameter^2 * π / 4

The formula of the area of a square

2*radius^2 or diameter^2

I had the formule ( M / N ) * 4

This is how I got it:

(d^2 * π / 4) : d^2 = M : N

π / 4 = M / N

π = ( M / N ) * 4

the problem is that I don't get pi as output, but about 14.2..

Does anyone know what I am doing wrong?

So in Processing I wrote the following code

float N = 0;
float M = 0;

void setup()
{
    size(400, 400);
    frameRate(90000); 
    background(255, 255, 255);
    ellipse(200,200,400,400);

}

void draw()
{

    /* Random x- en y-coordinate. */
    float x = random(0,400);
    float dx= (x-200);
    float y = random(0,400);
    float dy = (y-200);
    float d = (float)(Math.sqrt(Math.pow(dx,2) + Math.pow(dy,2)));

    /*Red in the circle*/
    if(d <= 200 ){ 
      stroke(255,0,0);
      M++;
    } 
    else{ 
      stroke(0,255,0); /*green around the circle*/
      N++;
    }
    point(x,y);
    println

    ((M/N)*4); 

}

Answer 1

The dots that land inside the circle also land in the square since the circle lays inside the square.

You need to do 4*M/(M+N).