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# Sierpinski Triangle Talk

I recently gave a lunchtime talk at a MathCounts competition, aimed at 6-9th graders, and I propped up my camera to take a low tech recording of the thing. The talk went quite well, and I want to post it here.

The title of the talk is “Anything worth doing is worth doing twice.” It’s about Sierpinski’s triangle (to the left), a beautiful and profound mathematical object, and how the different ways to construct the shape have yielded astonishing connections between different areas in mathematics (listen for the gasps from the audience).

Let me know what you think!

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1. Avery

Great talk! I think I’ve seen all of these generations at some point in the past, but I had forgotten the random walk and pascal triangle connection. Have you ever tried to do this in a classroom/exploratory way? Oh, one nit picky thing..you say that pascal’s triangle had the property of each number being the sum of the two numbers above it. Wouldn’t this be the definition of pascal’s triangle?

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Dan

Glad you liked it, Avery. I think I learned that random walk method back at Saint Ann’s, but I forget who showed it to me.

And as for your nitpicking: I usually define Pascal’s triangle by saying that the entry that goes in each spot is the number of ways to travel down to that spot from the top of the triangle. Or sometimes I define it as being generated by listing the m-dimensional subfaces of an n dimensional tetrahedron. We all have our favorite equivalent definitions, I suppose.

But seriously, I don’t put too much stock in what’s a property and what’s a definition: it always seems to me like an arbitrary way of picking your starting point.

2. Avery

Well I did warn you that it was nit picky. Do you have any idea what the original (historical) definition was? Was it even pascal?

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Dan

According to the wikipedia article, Pascal’s triangle was independently discovered by lots of different people in different places. They seemed to realize it was related to binomial coefficients very early.

I imagine that you’re right about the iterative definition being the standard one, historically. It’s so natural.

3. Denise

Love the talk!
But for the sake of showing it to students, I wish we could see the slides. I’ve seen these things before, so I can imagine what is happening behind your body, but I don’t think my 6th-grader would be able to follow it.

I’m tech-illiterate, so I don’t know how much work this would be, but could you make a vid with the soundtrack of your talk + the slide show?

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