Boredom in a fractal world

Brazilian butterfly Doxocopa laurentia (from Wikipedia)

A few of my students have been complaining that we don’t do enough different things from week to week for them to write a different newsletter article every Friday. PE, after all, is still PE, especially if we’re playing the same game this week as we did during the last.

So I’ve been thinking of ways to disabuse them of the notion that anything can be boring or uninteresting in this wonderful, remarkable world. A world of fractal symmetry, where a variegated leaf, a deciduous tree and a continental river system all look the same from slightly different points of view. A counterintuitive world where the smallest change, a handshake at the end of a game, or a butterfly flapping its wings can fundamentally change the nature of the simplest and the most complex systems.

“Chaos is found in greatest abundance wherever order is being sought. It always defeats order, because it is better organized.”
— Terry Pratchett (Interesting Times)

Fractal trees (from Wikimedia Commons)

There are two things I want to try, and I may do them in tandem. The first is to give special writing assignments where students have to describe a set of increasingly simple objects, with increasingly longer minimum word limits. I have not had to impose minimum word limits for writing assignments because peer sharing and peer review have established good standards on their own. Describing a tree, a coin, a 2×4, a racquetball in a few hundred words would be an exercise in observation and figurative language.

To do good writing and observation it often helps to have good mentor texts. We’re doing poetry this cycle and students are presenting their poems to the class during our morning community meetings. It had been my intention to make this an ongoing thing, so I think I’ll continue it, but for the next phase of presentations, have them chose descriptive poems like Wordsworth’s “Yew Trees“*.

Image from Wikimedia Commons

The world is too interesting a place to let boredom get between you and it.

* An excellent text for a Socratic dialogue would be the first page of Michael Riffaterre’s article, Interpretation and Descriptive Poetry: A Reading of Wordsworth’s “Yew-Trees”. It’s testing in its vocabulary but remarkably clear in thought if you can get through it.

Math map

When introducing the x,y coordinate system using a world map it is most effective if you use the right type of map projection. Most maps use a Mercator projection which stretches thing out as you get closer to the poles. You can see this in how the latitude lines get further apart as you get closer to higher latitudes and Antarctica and Greenland get all stretched out.

Mercator map from Wikimedia Commons.

The Mercator map is great for navigation, because if you measure angles on the map (bearings) between two places, you get the right bearing to sail your ship.

The better map to use for demonstrating the coordinate system would have an equirectangular projection, where all of the lines of latitude and longitude are equally spaced. These are harder to find, so I’m posting here a background map with the latitude and longitude marked on it (in 10 degree increments).

Equirectangular world map. Click on the image for a larger version. This is image is free to use if you cite this website (see cc-by-nc).

Notice the difference in sizes between the maps and the size of Greenland.

I’m also posting here, because it might be useful, a simple linear graph in Excel (or for OpenOffice) that simply plots lines if you enter the equation in slope-intercept form. There are lots of websites that let you do some really cool things (I’ll post about them later), but sometimes the simplest is what you want.

Geometry and the height of the mountains on the moon

Galileo's image of the moon
Galileo's map of the moon.

Galileo Galilei matched careful observation of sunlight and shadows on the moon, with some beautiful geometry to estimate the height of lunar mountains, in 1609. He needed the Pythagoras’ Theorem and the quadratic formula, both of which middle school students should be familiar. Larry Phillips has a nice post describing how Galileo did the math. The image below (from Pioneers of Science shows how to get started.

From the Gutenberg Project eBook of Pioneers of Science by Oliver Lodge.

The future of SketchUp

World Builder from BranitVFX on Vimeo.

Google’s SketchUp software is a great way to work on, and test, higher level geometry skills. This video is a well made, poignant introduction to what software like SketchUp could one day become. It has excellent story development, and has produced a great response from my students.