Month: February 2012

Week in Review – February 2012 Week 4

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Mathematics and Multimedia

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Using Paper Folding to Introduce the Notion of Proof

High School Geometry, High School Mathematics

Two years ago, I worked as part-time geometry instructor in a technical school near our university.  Most of the students in that school were quite clueless about the notion of proofs, so I tried to find ways to introduce proofs in an intuitive manner.

One lesson I developed was on proving that a quadrilateral formed from paper folding is a square.  I let the students create a square from a piece of bond paper without using any measuring instrument; only folding and cutting were allowed.

proof

As expected, most of the students used the method shown in the figure above. For the sake of discussion, we label the corners and critical points of the bond paper.  Most of the students constructed the square using the following steps (see figure): » Read more

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Create Polyhedra with Antiprism

Math Software, Teaching Tools

Last year, I shared about Archimedean, a user-friendly software in exploring solids and polyhedra.  If you want to create polyhedra with a little bit of challenge, you may want to try Antiprism.  Antiprism is a set of command line programs for working with polyhedra. There are programs to create, transform, analyze, and visualize polyhedra.


An extensive collection of polyhedra is included, many accessible by name: Platonic, Archimedean, Catalan, Johnson, uniform, prisms, antiprisms, pyramids, cuppolas, trapezohedra, uniform compounds, isohedral deltahedra, geodesic spheres.

The Antiview viewer allows a model to be inspected using various options, including a display of a model’s symmetry. The models may be exported to POV-Ray for producing high quality images, or to VRML for viewing on-line.

The programs are easily combined in scripts, making it easy to generate a series of models, or frames for an animation.

The Windows package is freely downloadable and freely redistributable. A source package is provided for users of other systems.

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