I bet you found filling out Pascal's triangle a bit tedious waaaaaaaaaaay before you hit the seventeenth row. I don't blame you one bit if you quit half-way. Some of the most interesting discoveries have come from tedious calculations.

The point was to see the pattern — adding two adjacent numbers in one row equals the number between them in the row below. For example, in the ninth row, the sum of 8 and 28 is 36. Below is what I did. You may want to print it for the first cool thing about Pascal's triangle.

The point was to see the pattern — adding two adjacent numbers in one row equals the number between them in the row below. For example, in the ninth row, the sum of 8 and 28 is 36. Below is what I did. You may want to print it for the first cool thing about Pascal's triangle.

pascalanswer.png |

There are so many things I love about Pascal's triangle. Today, I will hold back and only share two. The first cool trick is building a Sierpinski triangle by coloring only odd triangles in Pascal's triangle. If you print out the file above and color the odds, you can see the pattern emerge as you color.

The second cool thing requires you to add all the numbers on the same row. I've started it for you. By the time you reach the fifth or sixth row, you'll probably see another pattern emerge. Once you figure it out, you won't need to take the sum of a row because you can predict it from the sum of the previous row. Amazingly, this pattern is related to how ancient Egyptians multiplied numbers — something new that I learned this week. I put the answers for both printouts in the spoilers page.