Pascal's Triangle

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.

This application was developed to be a small 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 "^".

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!