## Thursday, July 4, 2013

### Euclidean Construction: Science vs Magic Makes it a Game

I liked high school geometry, but I've never taught a geometry course. And I feel limited when I try to do geometric constructions. Algebraic reasoning and coordinate graphs feel very natural to me. But the idea of constructing a pentagon, for instance, is a bit bewildering. I'm a bit clumsy with a compass and straightedge - I often push the pencil into the device and have to fix it and try again. So a site that lets me play with geometric construction without the mechanical device sounded intriguing.

The first time I heard about it (don't remember who, and don't know how to search my feedly reader the way I could with google reader), I tried it out and just got confused. There are minimal instructions on the site, and I just wasn't getting how to get started. So I went on to something else.

A few days later, Brent at The Math Less Traveled mentioned it, and explained the interface when I asked. I went back and played. There are 40 challenges in groups of 4. I've gotten through 21 so far and am looking forward to getting further. Nico Disseldorp, who created this site, has been working with Javascript for less than 8 months, and set this site up just a few weeks ago. I'm glad he got it out during the summer so I have more time to play.

The screen starts out with just two dots. Click on one and drag. You'll see a circle. If you drag to the other point it becomes a line segment. If you drag in any other direction and stop when the circle intersects the other point, the circle is fixed. Once you've drawn two circles, their points of intersection offer you new points to work from. The number of moves you've used so far is displayed at the bottom of the challenges box. (You can extend a line you've made without it counting as a new move.)

The first 4 challenges involve constructing a triangle. If you make one at all, you've completed one challenge. If you make one inside the first circle you drew, you've completed another. And if you make one in 8 or fewer moves, you've completed yet another. The last of the set of 4 challenges is to make the triangle in 5 or fewer moves. So the 40 challenges involve constructing 10 figures.

This is my construction of the 'circle pack 7'. It took me 17 moves, and there's a way to do it in 14.

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If you get excited about construction after playing here, and want a more flexible playground, you might like geometry toolbox.