The goal of today's class is to complete a computer program written in Java to draw pictures showing Pascal's triangle. We will show

• how math is used in coloring Pascal's triangle mod N to reveal patterns and
• how basic computer programming concepts and graphics programming concepts involve math.

The class:

• Exploring Pascal's Triangle
• Coloring patterns in Pascal's Triangle mod N
• Basic Facts about Pascal's Triangle from the Math Forum.

• Representing Pascal's Triangle as an array
• Basic Programming Concepts
• Pascal's array and picture in Java programming notation
• Programming lab to add Pascal drawing to a Java applet.

Additional Explorations:

• For more exploration with the mathematics of Pascal's triangle, go to the Math Forum link listed above.
• For more exploration of fractals and the relationship between Pascal's triangle and the Sierpinski triangles fractal, see Fractals, a collection of fractal lessons by Cynthia Lanius, including Why study fractals anyway?
• For more work with Java applets, go to this set of guided Java exercises at the Saturday Java Academy by Nancy McCracken. Note that this will require you to download some (free) software.