Park City Mathematics Institute 2006
Course Notes
Bowen Kerins and Ben Sinwell

Developing Mathematics: Some Applications of Geometric Thinking: While geometry is a wonderful field in its own right, geometric ideas are also useful tools for studying and understanding all kinds of phenomena inside and outside mathematics. Teachers in this course will look at some basic geometric habits of mind like studying continuous change and looking for things that don't change, and they'll apply these habits to a wide variety of situations. For example, we may look at

  • Geometric optimization: what are some general-purpose tools for minimizing paths or maximizing area?
  • Geometric invariants: what attributes of a figure stay the same when the figure is changed in some regular way?
  • The fundamental theorem of algebra: what does it say, why is it fundamental, and why is it true?
  • Fixed points: If you pick a positive number, take its square root, take the square root of that, and keep up the good work, what happens and why?
  • What geometric thinking is common to all these and similar questions?

No background with any of these questions will be assumed. One of the tools we may use in the course is a dynamic geometry environment (like The Geometer's Sketchpad® or Cabri). Here, too, we'll start from scratch. By the end of week three, we promise some beautiful and exciting applications of geometry.

June 26 - July 11, 2006
Download Day 1 - 11 [PDF file]

July 12, 2006
Download Day 12 [PDF file]

 

July 13, 2006
Download Day 13 [PDF file]

July 14, 2006
Download Day 14 [PDF file]

NOTE: As you select any of the links listed above, they will download as PDF files. To open PDF files use Adobe Acrobat Reader, available free from Adobe:

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© 2001 - 2014 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540.
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

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.