Java Programs for P1

// P1A
// Draws a logarithmic spiral with variable color..

import java.io.*;
import java.awt.*;

public class P1A {
   public static void main(String args[]) throws IOException {
      Drawing d = new Drawing();
	  d.resize(600,500); 
	  d.move(0,75); 
	  d.setTitle("Logarithmic Spiral");     
	  d.show();
	  }
   }

public class Drawing extends Frame {

   final int hc = 300;  
   final int vc = 250;    // (hc,vc) = center of the spiral
   
   
   final int n = 1000;    // The total number of "legs" in the spiral. 
   final int turn = 137;  // Turn factor. Each leg turns "left" this amount in degrees
   final double d = .4;   // The length of the kth leg is k*d
    
   public void paint(Graphics g) {
   
      int h, v;             // The horizontal and vertical coordinates of the current vertex.
      int h_next, v_next;   // The horizontal and vertical coordinates of the next vertex.
      int theta;            // The "angle" of the current leg.
      int k;                // The index of the current leg.
      double L;             // The length of the current leg.

      h = hc;
      v = vc;
      for (k=1;k<=n;k++) {
          if (k%3==0)
             g.setColor(Color.blue);
          else if (k%3==1)
             g.setColor(Color.red);
          else 
             g.setColor(Color.green);          
          theta = (k*turn) % 360;
          L = k*d;
          h_next = (int) Math.round(h + L*Math.cos(theta*Math.PI/180));
          v_next = (int) Math.round(v + L*Math.sin(theta*Math.PI/180));         
          g.drawLine(h,v,h_next,v_next);   // Draw the current leg.
          h = h_next;
          v = v_next;         
         }
      }
   }
 

 

// P1B
// Computes pi as a limit of polygon areas.

import java.io.*;

public class P1B {
   public static void main( String args[]) {
   
      // initialize Text object in to read from standard input.
      TokenReader in = new TokenReader(System.in);
	  
      int n;                   // The number of sides in the approximating n-gons.
      double OuterA, InnerA;   // The areas of the circumscibed and inscribed n-gons.
      double Error;            // OuterA - InnerA
      double c, s;             // The cosine and sine of pi/n.
      
      n = 4;
      
      OuterA = 4;
      InnerA = 2;
      c = 1.0/Math.sqrt(2.0);
      System.out.println("\n    n             A(n)                B(n)         B(n)-A(n)");
      System.out.println("-----------------------------------------------------------------");
      while (OuterA - InnerA > 0.00000001) {        
         n = 2*n;
         s = Math.sqrt((1.0 - c) / 2.0);  
         c = Math.sqrt((1.0 + c) / 2.0);
         InnerA = n*s*c;
         OuterA = n*s/c;
         Error = OuterA - InnerA;
         System.out.println(n + "   " + InnerA + "    " + OuterA + "    " + Error);
     }
     // Wait for user to enter input to ensure console window remains visible
     in.waitUntilEnter();
   }
}

// P1C
// Estimates pi via Monte Carlo.

import java.io.*;
import java.awt.*;

public class P1C {
   public static void main(String args[])  {
      Drawing d = new Drawing();
	  d.resize(600,500); 
	  d.move(0,75); 
	  d.setTitle("P1C: The Dart Board");     
	  d.show();
	  }
   }

public class Drawing extends Frame {

   final int hc = 300;  
   final int vc = 250;        // (hc,vc) = center of circle
   final int r  = 200;        // the radius
    
   public void paint(Graphics g) {
      
      int Left = hc-r;        // Left edge of square
      int Top  = vc-r;        // Top edge of square
      
      long k;                 // Dart throw index
      long hits;              // Number of darts that land in circle.
      long n;                 // Total number of darts thrown.
      
      double x,y;             // (x,y) = coordinates of current dart throw
      double dist;            // Distance of current dart throw to center.
      double MyPi;            // The pi-estimate.
     
      // Draw the target.
      
      g.drawOval(hc-r,vc-r,2*r,2*r);
      g.drawRect(hc-r,vc-r,2*r,2*r);
      
      // --------------- Comment Line A ----------------------
      
      hits = 0;
      n = 1000;
      for (k=1;k<=n;k++){
         // Generate the next dart throw and plot.
         x = Left + 2*r*Math.random();
         y = Top  + 2*r*Math.random();
         g.drawOval((int)x,(int)y,1,1);
         // Check to see if the throw lands inside the circle and tabulate.
         dist = Math.sqrt((x-hc)*(x-hc) + (y-vc)*(y-vc));
         if (dist<=r)
            hits++;
      }
      MyPi = ((double) hits/n)*4;
      Format.println(System.out,"Number of dart throws = %6d\n",n);
      Format.println(System.out,"Appx Pi = %20.15f",MyPi);
      Format.println(System.out,"True Pi = %20.15f",Math.PI);
      System.out.println();
      
      // --------------- Comment Line B ----------------------
      
      
      // --------------- Comment Line C ----------------------
       
      
    }
 }