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Other kids thought I was a bit different. And I guess they were right. I constantly drew in class, much to the chagrin of my teachers. The drawing was a useful talent when it came to such courses as geometry and art. But it did cost me some grades in history and English. Fortunately the spatial reasoning helped connect me to mathematics and I also found I had a head for numbers and symbol processing. I guess that's why I ended up a programmer.
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Take, for example, this drawing of roads intertwining. Some roads can be seen spiraling. Or the lines on the road can be seen coming off into space. Or merging.
My favorite illusion is the lines on the road becoming a thing unto themselves and floating in space. Even casting shadows.
My point is, if you see a kid drawing this kind of stuff, you might want to encourage it. Or at least try to understand what it is getting at.
In my case, my brain just wanted to make something interesting. The real world was kind of boring compared to what the imagination can provide.
The holes are interesting too. They represent negative space, and provide some contrast.
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So really it's more of an intellectual exercise. And its triangular clipped format makes it even more of an art piece.
All this was actually done without grid paper of any kind. Rather, I relied upon a ruler, a protractor, and a pencil. And I did have to erase some of my construction lines.
Hey, nobody's perfect!
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Still, minecraft is an excellent game for teaching spatial reasoning.
In this image, the hexagonal paper is used to create a fractal-like pattern. Really, it's closer to a space-filling curve. It's an example of the kind of fun I had in the 1980s.
The colors were simply drawn in with a set of felt pens. I don't think I have used the minimum number of colors. As we all know, four should suffice.
Shown on this yellow note paper sheet is a mesh construction of a face, a Hamiltonian unwrapping of a dodecahedron, and a picture of a dodecahedron (at the bottom) which has been stretched.
In the center is a rhombic dodecahedron constructed around a nesting cube, which can barely be made out.
To the left is a Hamltonian unwrapping of the same rhombic dodecahedron.
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Here are my sketched plans for it. It appears to be a corner-nested construction made of cubes. This should be familiar to any minecraft user.
Below it I have figured out how it can be folded flat (and this is one of the more interesting tasks that might be used to test spatial reasoning).
You cut the horizontal lines, and fold on the vertical lines to create the result. I was proud enough to save an actual example of the final product, which I unfolded and photographed.
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Actually I was kind of surprised it has survived.
And for my final trick, I have my self-portrait with copy machine. That's me at 16 or so. Probably about the time I went to UC Berkeley on the National Science Foundation seminar. And met Professor Lehmer. And got tear-gassed in a demonstration near the campus. And had to duck into Harry's Hofbrau. Where I was served a beer. But that's a story for another day.
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Should have posted this a while back....
ReplyDeletehttp://io9.com/5834081/people-who-doodle-learn-faster
another interesting one, whats really sticks wrote learning or hands on a tactile world?
ReplyDeletehttp://io9.com/5805127/geometry-is-hardwired-into-our-brains