Pascal's triangle has many secret treasures.
It yields the coefficients of the binomial expansion.
It can be used to predict probabilities in binomial trials.
It also has some beautiful patterns to reveal.

If you were to write out many rows of Pascal's
triangle and then circle the multiples of 2, you 
would notice a pattern.

If you were to write out many rows of Pascal's
triangle and then circle the multiples of 3, you 
would notice a different pattern was formed.

The enclosed program pascal is a program 32 bit C++ 
application that will help you visualize these patterns.
Twenty-nine rows of the pattern will fit on the screen. 
You may pick an integer and the program will "mark" each position of
the Pascal's triangle that is a multiple of the given
number with a "@".  Non-multiples will be marked with a
"^".

A dos version, pascal_.exe, of this program is included for non 32 bit
machines.  Twenty-seven rows of text will fit on the 
screen.  You may pick an integer and the program will 
"mark" each position of the Pascal's triangle that is a multiple of the given
number with a "8".  Non-multiples will be marked with a
"-". This version is not mouse controlled.  

Run the program and see the patterns for yourself.
See if there are any patterns to the patterns!

Compare the multiples of 2 & 3 with the multiples of 6.
Pay attention to the pattern formed by prime numbers.
See what you can discover!

Leslie Howe


Most Howe-Two software is designed using the mouse
controlled, user friendly interface provided by VB 
which will work on both 16 & 32 bit processor
machines.  This program has been written in C++ with a 
similar interface but is written for 32 bit machines.
The VB version of this program reveals the patterns with
contrasting colors and greater numbers of rows.

Visit http://www.usit.com/howe2 for more information
about instructional math software.







