Geometrical Concepts from Constructions, Models, and Investigations Summary

Monday, July 1, 2002

We started off introducing ourselves and talking about why we were interested in Geometry. We were very surprised to find that we had many things in common, the most surprising being that the majority of us teach out of Michael Serra's book, Discovering Geometry.

We also discussed a mission for our group.

  1. Expanding our own mathematical background
  2. Thinking about our own teaching
  3. Being a resource for other teachers

So, we're looking at going in two directions. First, we'd like to continue to polish our two projects from last year. Secondly, we'd like to pursue the idea of setting Philip Mallinson's PCMI Geometry problem sets from last year onto the web as a distrance learning class for teachers (and perhaps bright students). We plan to incorporate group members interests and passions into our work.

We then did some work with triangular numbers and deriving the formula for generating them: n(n + 1)/2. We also looked at Pascal's triangle and noticed that on the diagonals we have linear numbers, triangular numbers and tetrahedral numbers.

As a reference we looked at figurative numbers from John Conway's The Book of Numbers.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.