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Another lesson re the HexaPent
Posted:
Jul 6, 2006 7:29 PM
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Reposting from Gnu Math Archives (4dstudios.2006).
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Preview of what this is about:
http://photos1.blogger.com/blogger/1134/545/1600/30freq.png
BACKGROUND:
Back in March, I was sharing about gnu math teacher Glenn Stockton's cube-cell to hexapent mapping:
http://mathforum.org/kb/message.jspa?messageID=4559477
Given Glenn's cryptography background, I can understand why he's focused on these tabular XY matrices, stacked on a Z axis to give a cube. However, I think with many kids, this'll be too abstract an approach initially, and we need a better way to access hexapent geometry.
The Chattanooga Aquarium introduces this geometry via turtle shells, which is a good way to go. Radiolaria are another popular item. However, I think Glenn has another idea that'll fly with many students: a grid on a globe.
Using open source tools, a gnu math teacher might introduce several important skills, along with relevant concepts.
We want to reinforce angle (shape) vs. frequency (scale), as well is viewpoint (inside looking out vs. outside looking in). Ray tracers are good for this, as they don't let you forget about the viewpoint (the camera).
As the cubists tried to remind us (Picasso et al), an object seen from all sides at once is a myth, as trying to paint that way makes obvious.
Anyway, I've posted blog entries showing hexapent globes in two frequencies, which you're free to reuse in your own web based presentations:
http://controlroom.blogspot.com/2006/07/global-matrix-poster.html
http://controlroom.blogspot.com/2006/07/hexapent.html
You don't need to include me in your credits, as I simply combined two web resources in an obvious manner (follow links in the caption).
Topics you might want students to practice discussing:
(a) the generic geometrical challenge of getting a spherical object displayed on a flat surface (cartographic projections thread)
(b) the concept of "geometry in nature" and the design philosophy which would have us look to nature herself for good ideas (can you think of other examples?)
(c) the Geoscope concept (we've gone into that elsewhere, so no need to repeat myself here -- gnu math teachers are generally up on what's in 'Critical Path' after all).
I'm sure you can think of others.
Kirby
PS: The Globe Project from Design Science Toys is now a collectors item, if you're lucky enough to have one, ever since DST went up in flames.
http://imagemission.com/en_dst.htm
http://www.wonderbrains.com/globe-project.html
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