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Construction and
enumeration of Franklin circles
Rebecca Garcia, Stefanie Meyer, Stacey Sanders and Amanda Seitz
Vol. 2 (2009), No. 3, 357–370
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Abstract |
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Around 1752, Benjamin Franklin constructed a variant on the popular magic squares and what we call a magic -circle. We provide a definition for magic -circles, magic -circles and, more specifically, Franklin magic -circles. In this paper, we use techniques in computational algebraic combinatorics and enumerative geometry to construct and to count Franklin magic 8-circles. We also provide a description of its minimal Hilbert basis and determine the symmetry operations on Franklin magic 8-circles. |
Keywords
Franklin squares, Franklin circles, magic circles,
enumeration, polyhedral cones, Ehrhart series
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Mathematical Subject Classification 2000
Primary: 05A15
Secondary: 15A48
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Milestones
Received: 15 March 2009
Revised: 6 June 2009
Accepted: 6 June 2009
Published: 3 October 2009
Communicated by Scott Chapman
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Authors |
| Rebecca Garcia | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
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| http://www.shsu.edu/~mth_reg | |
| Stefanie Meyer | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
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| Stacey Sanders | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
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| Amanda Seitz | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
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