Day 24, MAT115

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Announcements:
- Today we'll finish up with fractals by considering them in the context of Pascal's triangle.
- I've given you a homework assignment for Friday. Try a few fractals!
Question of the Day:

How are the Sierpinski and Pascal Triangles related?
Let's review what we learned about last time:
1. We began by talking about the homework. In particular, I showed how one might compute how many rabbit pairs there are in the "mortal rabbits" homework problem, by using properties of fractals. We'll use that idea again today.
2. Last time we talked more about area fractals: how the Golden rectangle is fractal; how one can create new fractals with rectangles (e.g. the Harriss fractal)
3. We also created an area fractal, based on triangles.
In each case, there's "the world within the world": that's the most important property of fractals.
We'll start off new material today by learning the Sierpinski triangle (another area fractal).
- By subtraction
- After we're finished removing all that stuff, how much area is left in the triangle?
Of course, Sierpinski's triangle is "infinitely deep".... (You need to listen to the Doors, or Jefferson Airplane, or Jimi Hendrix while studying fractals.)
Now back to Pascal's triangle. What does it have to do with Sierpinski?
We'll get to that in a moment, but first I want to remind you how it's related to Fibonacci numbers. If you did your reading, you already know!
I'll also remind you about its relationship to Plinko and see another reason why the row sums are powers of 2.
Now, I want to introduce you to Vi Hart, who will talk us through the relationship between Pascal and Sierpinski. She talks really fast, however!

Links:

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