The other day in class during an exploration into solid geometry, we discovered we could make these lovely flowers
by smashing the paper cones we had made.
Now, if I can just figure out how to test the students on this material.
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Challenge Geometry
Fun With One Cut
Inspired by a brilliant talk by Erik Demaine, I started playing around with the famous one-cut problem: given a shape made up of straight line segments, can you fold the paper flat in such a way that with only one straight cut your shape will appear?
Having no real experience with mathematical paper folding, I thought I’d try out a Koch Curve. Well, a finite iteration of it, at least.
It seemed like the strategy was to use the symmetry of the shape to make all the line segments line up on each other. So I folded down the middle, and then again down the new middle.
I rotated the last shape and it seemed a little clearer how to continue.
It seemed like all the lines were lined up, so to speak. So I cut. And voila!
Not too bad! Now, if I could just figure out how to do this with non-symmetric figures.
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Appreciation Geometry Photography
Math Photo: Rooftop Midline
This photo reminds me of my favorite theorem from elementary geometry: if you connect the midpoints of two sides of a triangle, the segment is both parallel to, and half the length of, the third side.
You can find out a little more about this theorem here.
Geometry Resources
Amazing Fractal Video
This video is billed as “an evolving landscape of a 3D fractal surface”.
I’m not sure exactly what that means, but it’s awesome. And the author claims to be working on some kind of fractal explorer that presumably would allow the user to navigate around the object.
Appreciation Geometry Photography
Math Photo: Strange Surface
Today’s Challenge: Describe this surface mathematically!
