# WCYDWT: Geometry in Geography

As I was flying home from the 2012 NAIS Annual Conference in Seattle, I looked out airplane’s window and saw these patterns in the farmland below. I’m going to figure out a way to use them in my geometry classes. We just finished learning about areas of polygons and circles, so I’m sure these pictures can spark some interesting questions and investigations.

By the way, WCYDWT stands for “What Can You Do With This”, a teaching technique pioneered and championed by Dan Meyer. There’s a permanent link to his blog at the bottom of my home page.

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# Light, Camera, Hyperbola!

It’s relatively easy to photograph behavior that models a parabola – you can photograph the stream coming out of a water fountain, for example.

Ellipses aren’t so difficult to find either, especially semi-ellipses.

However, a visual representation of a hyperbola is a little tougher to find. Here’s photo I took of a flashlight against a wall. The flashlight’s cone of light is intersected by the vertical wall, and the upper half of a hyperbola is clearly visible!

I pasted the image into Geometer’s Sketchpad, and plotted three points. Using the points’ coordinates and a lot of substitution, I was able to come up with a function that matched the edge of light fairly closely:

Now we’ll have to see if my Precalculus students can do it!