Mathematical Foundation: Modular Arithmetic

First, I will introduce the notion of modular arithmetic, "clock arithmetic", based on division-with-remainder. x (mod_n) = the remainder when x is divided by n.

(x+_modn y) = (x+y) (mod_n)

(x*_modn y) = (x*y) (mod_n)

Then we will color Pascal's triangle mod₂, with a color for even numbers and another color for odd numbers. Upon completion, we will discuss why the arithmetic results are the same(!) as the designs we drew yesterday.

Today's work will lead into our work in "number bases".

Homework: Color-by-remainder the triangle for a different number instead of 2. think about how the image is similar and different from the one we did in class. Also, practice a few modular arithmetic porblems.