CS 100: Programming Assignment P1
Solution
// 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(1000,800); d.move(0,75); d.setTitle("Logarithmic Spiral"); d.show(); } } public class Drawing extends Frame { final int hc = 500; final int vc = 350; // (hc,vc) = center of the spiral final int n = 1000; // The total number of "legs" in the spiral. final int turn = 150; // Turn factor. Each leg turns "left" this amount in degrees final double d = .5; // 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. double 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++) { // Determine the color of the kth leg. if (k%3="=0)" g.setColor(Color.magenta); else if (k%3="=1)" g.setColor(Color.cyan); else g.setColor(Color.green); // Determine the endpoints and draw. theta="(k*turn)*Math.PI/180;" L="k*d;" h_next="(int)" Math.round(h + L*Math.cos(theta)); v_next="(int)" Math.round(v + L*Math.sin(theta)); g.drawLine(h,v,h_next,v_next); h="h_next;" v="v_next;" } } } // P1B // Estimates pi as a limit of polygon areas. import java.io.*; public class P1B { public static void main( String args[]) { 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); Format.print(System.out,"%5d ",n); Format.print(System.out," %15.9f ",InnerA); Format.print(System.out," %15.9f ",OuterA); Format.println(System.out," %6.2e ",Error); } System.out.println(); } }
// P1B // Estimates pi as a limit of polygon areas. import java.io.*; public class P1B { public static void main( String args[]) { 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); Format.print(System.out,"%5d ",n); Format.print(System.out," %15.9f ",InnerA); Format.print(System.out," %15.9f ",OuterA); Format.println(System.out," %6.2e ",Error); } System.out.println(); } }
// 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; // 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 ---------------------- n = 100; 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); } // --------------- Comment Line B ---------------------- hits = 0; n = 100000; 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(); // 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 C ---------------------- } }