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Virginia State University

Title: Geometric Triple Systems

Directors: Dawit Haile and Raymond Fletcher

Email: dhaile@vsu.edu and rfletcher@vsu.edu

Dates of Program: May 14 ? June 22, 2012

Summary:

Let k ’ Zn. If n points in the plane, labeled with Zn, are arranged so that all subsets {{a, b, c}: a + b + c = k} correspond to collinear triples, we say that the n points form a geometric triple system T(Zn, k). The geometric triple system T(Z, k) is defined similarly on the set Z of all integers. Geometric triple systems arise naturally in the study of perfect polygons and share some of the properties of perfect polygons. For example, all the vertices of a perfect polygon as well as all the points of a geometric triple system lie on a cubic curve.

During the six-week summer undergraduate research work, students will use Geometer?s Sketch Pad to make various ad hoc constructions of geometric triple systems and to determine isomorphisms. They will use the Theorems of Desargues and Pappus to prove some of their constructions. Students will then prove the existence of geometric triple systems by constructing them on a given cubic curve. Finally, students will be led in an investigation of the connection between geometric triple systems and perfect polygons.

Student Researchers Supported by MAA:

  • Hope Gibbs - Virginia State University, VA
  • Dustin Robinson - Virginia State University, VA
  • April-Nicole Smith - Virginia State University, VA
  • Kristin Strand - Virginia State University, VA
  • Carson Wang - University of Virginia, VA
  • Willie Williamson - Elizabeth City State University, NC

 

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

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