Saturday, September 22, 2012

Double-check your napkin

The 2011 movie Contagion required viewers to appreciate the speed at which infection can spread.  The term “R-nought” is used to represent the reproductive rate: If R0 = 2, then each infected person infects two more.  So R0 is the base of the exponential function y = R0^x, where x is the number of time steps.  However, Jude here seems to have a different take on the function, spitting out the terms 2, 4, 16, 256, …

You might think about asking your students

  • In the sequence 2, 4, 16, 256,…
    What are the next several terms?  Is the 30th term close to a billion?  What is the recursive formula for the sequence?
  • If you start with 2 infected people, and each infected person will infect 2 others, give the number of new infections for the first few time steps.  What about total infections for the first few time steps?  Can you figure out how many people will have been infected after 30 time steps?

Friday, September 14, 2012

Harmonigraph revisited

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A harmonigraph is still on my To-Build list (have you seen one yet?), so I’m still making do with a simulation.  I tweaked my first attempt to make it even awesomer. 

Now the color changes over time, and I narrowed down the possible periods for the pendulums, and it’s not so boring to watch because it’s super fast.  Try it out - click two places to get a new image (try two close to center).

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This simulation uses the parametric equations
x = sin (A t) + sin (B t)
y = cos (A t) + sin (C t)
with the period of each component limited to a value between 2 and 2.5. 

Saturday, September 8, 2012

Managing supplies

Now that school’s back in session, you may be noticing that your neatly arranged classroom supplies tend to fair better when students are at home.  After I noticed my scissors slowly dwindling in number, I began storing them in a 2x4.
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I made some more holders like this for markers, and they worked pretty well.  The kids dubbed them “pen islands,” and the inappropriate name stuck.

Feeling more industrious, I came up with this industrial-sized tape dispenser.  The roll of tape was $5 at a hardware store and lasted at least 4 years.
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