Advanced Geometry Summary

Monday - Friday, July 10 - 14, 2006

Monday and Tuesday were the only working days for the group, since Thursday was the presentation day and Friday was a special all-institute program honoring Herb Clemens. Thus in addition to the course time, we only had 2 hours for discussion this week.

In the Colin Adams class we learned about the genus of a knot, which is the smallest genus of the various Seifert surfaces with boundary equal to the knot.

Also, we pursued the "human knot" theme to a new level, with a choreographed knot made of 3 rings of humans.

In the discussion time, we did discuss some of the new theory we learned, but we spent an increasing amount of time discussing how knots could be used in K12 classes and then what to put in our presentation Thursday. In addition to the lesson developed by Henri Picciotto, we decided to demonstrate a human tangle and inverse tangle.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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