Sunday, February 14, 2010

Triangle problem...again

Hey, you haven't answered my first triangle problem, but here's a related video to inspire you:

Scientific notation in Avatar

Despite complete disregard for their work by leadership, scientists are the heroes of Avatar.  And who better to teach scientific notation?
GRACE: Alright, look -- I don’t have the answers yet, I’m just now starting to even frame the questions. What we think we know -- is that there’s some kind of electrochemical communication between the roots of the trees. Like the synapses between neurons. Each tree has ten to the fourth connections to the trees around it, and there are ten to the twelfth trees on Pandora --

SELFRIDGE: That’s a lot I’m guessing.

GRACE: That’s more connections than the human brain. You get it? It’s a network -- a global network. And the Na’vi can access it -- they can upload and download data -- memories -- at sites like the one you destroyed.

So we multiply 104 and 1012 (perhaps dividing by 2 so as not to count connections twice), and get 1016 (within 1 order of magnitude).  A 1988 article in Annual Review of Neuroscience suggests a human brain has  100 billion (1011) neurons and 100 trillion (1014) synapses, so the Avatar claim seems reasonable.

Can we quantify human memory like this?  Yeah, probably.

Thursday, February 4, 2010

Pascal in Excel

As an enrichment activity I had a student fill a large sheet of graph paper with Pascal's triangle - just the ones digits, anyway.  Then he colored the digits in different ways to discover patterns.  After doing this by hand, the student was interested in saving some time with Excel, so I devised this method:

  1. Make a grid of 0's.  Really you just need a border of 0's, but filling an area is faster.  It should be twice as wide as tall.

  2. Select cell B2, and give it the formula =MOD(A1+c1,10).
    pascalexcel1

  3. Copy B2 and paste it into all the cells in the grid except for the top row and the left and right columns.

  4. Now they are all adding the values of the two cells diagonally above them.  Just put a "1" in the middle of the top row and see what happens.
    pascalexcel2

  5. To color the different digits, click Format, Conditional Formatting, and make some stuff up.
    pascalexcel3

  6. I changed the font color to white and clicked File > Web Page Preview:
    pascalexcel4


You could do some fun experiments with this, leading kids toward the idea of cellular automata!