I think that I shall never see / a poem lovely as a^2+b^2 equals the square of c

So its winter break now, fall term ended about a week ago.  I taught two classes again this term but unfortunately they were on the opposite sides of town.  Luckily, Sugar took classes at both schools so we were able to work out a car pooling schedule back and forth.  As far as how difficult it could have been, it was not that.  There were a few surprising challenges, though–like making sure I had done laundry, or figuring how much food to buy at the grocery store so that I could eat it before it went bad given that I rarely spent time at my house, let alone meal times.  Anyway, it worked out, we are on break and I have two classes at the same school next term.

One of the classes I taught was called Math in Society — a somewhat remedial math class for students not planning on pursuing anything scientific.  I affectionately called it Math for Poets, although now that I think about it, we didn’t do nearly as much poetry as we should have.  We covered some probability and stats, and money math–stuff useful for everyday life–but we also did some logic and explored the golden ratio and we got to do some math in music.  Here are some of the ::notes:: I made up for the class, and while you’re reading them, it could be helpful to get a couple of ::pure tone generator:: windows open to listen to the examples.

An update on a ::previous entry::--I’ve kept working on generating a Mandelbrot set, and I’ve since gotten it to ZOOM!

 

Also on the Fractal programming front, I’ve been reading a book about Chaos and Fractals that pointed me in the direction of this simple algorithm:

  1. Draw three triangles on a piece of paper, call these ‘bases’ and number them A, B and C.
  2. Draw a fourth random point on the paper.  This is called the ‘game point’
  3. Roll a die to randomly select one of the bases (if you roll a 1 or 2, select base A, if you roll a 3 or 4, select base B, if you roll a 5 or a 6, select base C.)
  4. From the game point, draw an imaginary line to the base selected in the previous step, and actually plot the midpoint (halfway point) on that line.  This is the new game point.  Repeat steps 3 and 4 as many times as you want.

If you do this enough times, regardless of the original points, you will see a similar pattern emerge.  This pattern is called the Sierpinski Gasket. Below are a couple of generated images with various bases.

In adventure news, we were able to squeak in one more hike to Mt. Pilchuck for Sugar’s birthday in September, we spent most of the hike with blue skies until we got to the very top, and clouds covered our views.   We also saw jazz legend Wayne Shorter, and went to an underground amateur wrestling match.    I just got back from visiting family in Iowa to celebrate my grandma’s 80th birthday!  I submitted grades and now we are spending our winter break dog-sitting for a couple of friends, but Sugar is really sick, so we’ve been relaxing.  And I also finished another cutout project, this time a sunflower.

Merry Christmas and Happy New Year!

 

 

 

 

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