November 17, 2009
Tom Banchoff is known for his research in differential geometry in three and four dimensions and for his efforts to develop methods of computer graphics. He has authored and co-authored numerous fascinating books. He also has a new book coming out in January.
Tom's presentation included a viewing of Flatland the movie (he is a consultant on the project). This is an updated, much-improved film version of Edwin Abbott's 1884 classic satirical book Flatland: A Romance of Many Dimensions.
Tom distributed a handout for students to use for discussion following the film. This link includes notes for teachers.
There is an article about slicing cubes and hypercubes that includes some exercises similar to the slicing activity we discussed in the session.
Because this article includes interactive applets, it is necessary to open it from Tom's website. Click here for the article. It will take a few moments for this link to open because it is so rich with graphics. Discussion of the concept of dimension followed. We discussed cross sections of an "infinitely-long" stick of butter, visualizing the possible polygons that could be found.
During our discussion of 3-dimensional drawings, Dr. Banchoff shared some of the wonderful renderings included on his website. Click here for a link to his page. He also mentioned his student, Cassidy Curtis, who submitted the Best Homework Ever. Click here to see Cassidy's work.
Performance and process standards addressed in the presentation Include:
4.1.2 Visualize solids and surfaces in 3-dimensional space when given 2-dimensional representations.
4.1.3 Create and analyze arguments concerning geometric ideas and relationships.
4.2.1 Model the result of rotations of a 2-dimensional figure.
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| Tom sketches a cross-section of a stick of butter. | Mandy Forslund and Carolyn Hollis discuss possible cross-sections. | Tom illustrates a rhombus. |
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| The catered dinners are an especially nice feature of Teachers' Circles. |
