Math Art

Triangle Example

Suppose that you want to make the following pattern on the screen:

*
**
***
****
*****

Build it up from small pieces. Start with what you know, build slowly.

1. You notice that the number of stars on each line makes the following pattern:

2. You start with a basic program, labelling the end } so you can track them:

public class mathArt
{
   public static void main (String args [])
   {  new mathArt ();
   } //main

   public mathArt ()
   {
   } //constructor
} //class

3. You add a loop to print out the numbers 1 to 5.

public class mathArt
   {
   public static void main (String args [])
   {
     new mathArt ();
   } //main

   public mathArt ()
   {
     int counter = 1;
     while (counter < 6)
     {
       System.out.println (counter);
       counter++;
     }//while outer
   } //constructor
} //class

4. You change the loop to have another loop inside that prints out 1 of 1, 2 of 2 etc. For example: 122333444455555. The outer loop handles the variables moving from 1 to 2 to 3 to 4 to 5. The inner loop handles the printing of one 1, two 2s, three 3s etc.

public class mathArt
{
   public static void main (String args [])
   {
      new mathArt ();
   } //main

   public mathArt ()
   {
     int counter = 1;
     while (counter < 6)
     {
        int counter2 = 0;
        while (counter2 < counter)
        {
          System.out.print (counter);
          counter2++;
        } //while inner
        counter++;
     } //while outer
   } //constructor
} //class

5. Your next step is to switch the System.out.println(counter) to print a star. Then, you make an enter print after every line ie in the outer loop.

public class mathArt
{
    public static void main (String args [])
    {
        new mathArt ();
    } //main

   public mathArt ()
   {
     int counter = 1;
     while (counter < 6)
     {
       int counter2 = 0;
       while (counter2 < counter)
       {
         System.out.print ("*");
         counter2++;
       } //while inner
       System.out.println();
       counter++;
     } //while outer
   } //constructor
} //class

You're finished.

Process summary:

1. Figure out a sequence of numbers that represents your pattern
2. Develop a basic program
3. Develop an outer loop that counts the number of lines you need
4. Loop the inner loop to print the pattern that you need
5. Format as required with symbols and plank lines.

Other Examples:

Box Example

import java.applet.Applet;
import java.awt.*;

public class MathArt extends Applet
{
   public void paint (Graphics g)
   {
     int x = 15;
     int y = 15;
     int count = 1;
     while (count < 26)
     {
       g.drawRect (100, 100, x, y);
       x += 5;
       y += 5;
       count++;
     } //while
   } //paint
} //class

• the items in blue manage the loop
• the items in red manage the loop's functions. Which is, printing out the boxes.

Changing Colour Example

public void paint (Graphics g)
{
         int x = 15;
         int y = 15;
         int count = 1;

         while (count < 6)
         {
            g.drawRect (x, y, 25, 25);
            x += 30;
            count++; 
         } //while inner

 } //paint

public void paint (Graphics g)
{
       int x = 15;
       int y = 15;
       int count1 = 1;
       int count = 1;       

       while (count1 < 5)
       {
         while (count < 6)
         {
            g.drawRect (x, y, 25, 25);
            x += 30;
            count++;

         } //while inner

         x = 15;
         y += 30;
         count1++;
         count = 1;
       } //while outer
} //paint

public void paint (Graphics g)
{
         int x = 15;
         int y = 15;
         int count1 = 1;
         int count = 1;
         
         while (count1 < 5)
         {
            while (count < 6)
            {
              g.setColor (new Color (0, 0, 255));
              g.fillRect (x, y, 25, 25);
              x += 30;
              count++;
         
            } //while inner 

         x = 15;
         y += 30;
         count1++;
         count = 1;
} //while outer

public void paint (Graphics g)
 {
      int x = 15;
      int y = 15;
      int count1 = 1;
      int count = 1;
      int blue = 255;  

      while (count1 < 5)
      {
         while (count < 6)
         {
           g.setColor (new Color (0, 0, blue));
           g.fillRect (x, y, 25, 25);
           x += 30;
           count++;
           blue -= 10;

         } //while inner

         x = 15;
         y += 30;
         count1++;
         count = 1;
       } //while outer
} //paint