I first encountered Pascal’s triangle on a worksheet my older brother brought home from school when I was in eighth grade. At the time, I was taking geometry (with a teacher who had a cool pair of ...

Rows zero through five of Pascal’s triangle. The pattern continues on into infinity. Two of the sides are filled with 1's and all the other numbers are generated by adding the two numbers above.

So if we use the formula for choose, Pascal's triangle becomes this. Compare it with the picture of cube slices. Amazingly, the number of vertices within each cube slice directly corresponds to ...