Park City Mathematics Institute
Geometrical Concepts from Constructions, Models, and Investigations

Circle Packing: A Directed Investigation of Descartes' Circle Theorem
Celeste Williams

Teacher Directions || Worksheet
Download:
    finalcirclepacking.doc - MS Word
    finalcirclepacking.pdf - PDF format
    circlepackingworksheet.doc - MS Word
    circlepackingworksheet.pdf - PDF format

WHAT IS IT?
Descartes' Circle Theorem involves relationships among radii of tangent circles, "packed" together. The relationship is expressed using the curvature of each circle, which is also the reciprocal of the radius involved.

GRADE LEVEL/STRAND
The lesson is designed for high school geometry students who have studied tangent circles.

CLASS TIME
The lesson is designed to be done outside of class as a directed investigation.

MATERIALS
No materials are required but the investigation can be done with the help of The Geometer's Sketchpad®.

OBJECTIVES

  • Increase understanding of the curvature of a circle and its relation to creating tangent circles packed together.
  • See what can be learned from Descartes' Circle Theorem.

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    IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
    at the Institute for Advanced Study, 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.
    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.