|
|||||
 |
|
|
|
|
Construction and
enumeration of Franklin circles
Rebecca Garcia, Stefanie Meyer, Stacey Sanders and Amanda Seitz |
|
Vol. 2 (2009), No. 3, 357–370
|
Abstract |
|
Around 1752, Benjamin Franklin constructed a variant on the popular magic squares and what we call a magic (a,r)-circle. We provide a definition for magic (a,r)-circles, magic a-circles and, more specifically, Franklin magic a-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
|
Mathematical Subject Classification 2000
Primary: 05A15
Secondary: 15A48
|
Milestones
Received: 15 March 2009
Revised: 6 June 2009
Accepted: 6 June 2009
Published: 3 October 2009
|
Authors |
| Rebecca Garcia | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
|
| http://www.shsu.edu/~mth_reg | |
| Stefanie Meyer | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
|
| Stacey Sanders | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
|
| Amanda Seitz | |
| Sam Houston State University Department of Mathematics and Statistics Box 2206 Huntsville, TX 77340 United States |
|
|
