This week in Math, Art, & Design, we built things in 3D, primarily out of triangles. We found out that it is possible to fold both triangles and tetrahedra out of paper plates. Then we used the tetrahedra to make an open icosahedron (scroll to the bottom of this link). We then used paper plates in another way to make another kind of icosahedron (see the class challenges for details). We also talked about what can be made of triangles (including sphere-type shapes and shapes with curvature like a Pringles potato chip of the inside of a donut) based on faces and then switched to straws and pipecleaners. Finally, I showed a short clip about Buckminster Fuller and one about Margaret Wertheim’s crocheted hyperbolic geometry.
Here are the notes on challenges from this week’s class. Before next week, you should do a response to this week and email it to me, or bring it to class. Class responses should be about 350-600 words if you are writing them, but you are welcome to do something else that responds to the class (visual, video, audio, etc). Some things to consider responding to:
- Did you discover/build anything interesting during class? What made it interesting?
- Where have you seen or used polyhedra out in the world? In art or design?
- Consider responding to any of the challenges you found interesting or challenging.
- Consider exploring and responding to some of the links below.
- What are you interested in learning more about that is connected to geometry or mathematics?
Other sources and links for this week, some of these make good material for projects:
- More circle folding: https://www.thefutureschannel.com/pdf/math/circle_folding.pdf
- Even more circle folding: http://www.mi.sanu.ac.rs/vismath/hansen/index.html
- Polyhedra, including some of the naming conventions: http://www.geom.uiuc.edu/docs/education/institute91/handouts/node6.html#SECTION00060000000000000000
- 3D paper sculptures: http://tag.wonderhowto.com/3d-paper-sculpture/
- Folding and unfolding polyhedra: http://plus.maths.org/content/os/issue27/features/mathart/index
- Paper models of polyhedra: http://www.korthalsaltes.com/
- Modular Origami, another way to make polyhedra:
- Sonobe (we did this in Tue/Th class but not Mon class)
- Folding/using PHiZZ video (then can continue to part 2)
- Making buckyballs video
- Making the torus (doughnut) (88 PHiZZ units): http://www.usd.edu/arts-and-sciences/math/upload/Euler-formula-torus.pdf the blueprint for the torus is on p. 7.