Pascal's_Triangles_Mod

Pascal's triangle is an arrangement of numbers with a simple rule for production that yields the binomial coefficients.

The (k-1)st number in the nth row is the number of different ways that you can choose k items from a set of n items. For example, suppose you have 10 people and you need to make a committee of three people there are 10 choose 3 different committees. go to the 10th row and count out 3+1 or 4 numbers and see that there are 120 different committees you could make.

These numbers also give the coefficient of x^k y^n-k term in the expansion of the binomial (x + y)^n

If the addition in the rule for producing Pascal's triangle is done mod n then it is possible to color the positions with n colors and make a colored triangle with interesting patterns. The patterns are very different for different values of n. Click Here to see hexagons made from six of Pascal's modular triangles for n = 2 to 16. Click here for the same hexagons in different colors.