Friday, April 29, 2011

Magazine Project Topics

So far, here are the topics my kids have chosen for their Geometry magazine articles:
1 group is doing an article on fiberoptic cables -- their history and also how they are an application of the concept of reflection.

1 group is doing an article on geometric paradoxes. Even though I was picturing them doing paradoxes such as how the Koch fractal is a finite area with an infinite perimeter, for now they're focusing on visual illusions that show that when you re-arrange puzzle pieces to make the same shape, there is a gap in the new "congruent" shape. They're going to use examples from the web, but add their own explanations for why the "illusion" works.

1 group is researching perspective drawings -- what different types (1-point, 2-point, 3-point, etc.) there are, how they differ, and where they are most commonly used.

1 group is researching tessellations -- what makes a shape tessellate and what natural objects (such as beehives) tessellate.

1 group is doing an article on triangulation vs. trilateration -- what are the differences, and what are some modern applications of each?

1 group is focusing on "simple" (ie. right-triangle) trigonometry and its common applications. I recommended looking into the vector stuff in physics, since they seem interested in knowing why all engineers need to learn trig.

1 group is doing an article on sinusoidal waves -- their math discussions will include basic features of a wave function (amplitude, frequency) and how they are represented numerically as transformations to sine or cosine. Their extension will be focused on light waves and its modern applications.

2 groups are working on the applications of fractals. (We recently saw a video on fractals, so they are very interested in researching it further. I told them that they could do the same topic, as long as their actual article content does not overlap.)

1 kid is planning out a two-page comic strip story about the life of Pythagoras.

1 group is doing Pythagorean Theorem -- not sure what their deal is, since they still need to find a narrower focus, but I think eventually they might settle on discussing the various visual proofs of Pythagorean Theorem. (They were looking at some of that stuff on the web and thought it was "so cool"!)

1 group is doing symmetry. I tried recommending them to take a look at the concept of beauty with symmetry, but last I checked they were looking at flags..

1 group is doing how architects use Geometry and software to design buildings. One of their dads is actually an architect and has knowledge / access to AutoCAD. Could be promising.

1 group chose to write about geometric spirals. I was thinking more along the lines of them researching Spirals of Theodorus and other such spirals made of triangles, but they seem to have found some other ones.

1 group (who waited till last second to pick a topic) really hated all of the remaining topics on the list. So, I recommended them looking into spherical geometry. Now they seem to think it's pretty neat, since it debunks a lot of their "duh" ideas of Euclidean geometry.

Anyway -- I'm excited! :) I'm fully expecting their first drafts due next Friday to need a lot of work, but I think it's promising that they find their research topics interesting. The only thing I am a little nervous about is the timing. We have roughly 1 month before finals, and I don't want my volunteer editor and webmaster to still be assembling the magazine and the website while their other teachers crank up the heat before finals. We're going to have to be REALLY on top of the deadlines in order to avoid that!!

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