Sona Sand Drawings and Permutation Groups

Year: 2001 Authors: Mark D. Schlatter

Core claim

Permutation-group representations and word reductions can characterize monolinearity and curve counts for sona sand drawings and related mirror-curve constructions.

Topics

sona sand drawings, monolinearity, permutation groups, mirror curves

Domains

group theory, combinatorics, geometric transformations, pattern design, mat designs, visual geometry

Methods

word reduction, sequence analysis, polygon transformations

Media

sand drawings, regular polygon, plaited mats

Paper text

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BRIDGES Mathematical Connections in Art, Music, and Science

Sona Sand Drawings and Permutation Groups

Mark D. Schlatter Department of Mathematics Centenary College of Louisiana 2911 Centenary Blvd. Shreveport, LA 71104 Email: mschlat@centenary.edu

Abstract

We will examine sona sand drawings (as presented in the work by Paulus Gerdes [1]) and the conditions that guarantee monolinearity – the property that the curve can be traced in one continuous motion. In particular, we will discuss plaited mat designs and generalized lion’s stomach designs. We will associate words from permutation groups with these designs and use reductions of these words to determine the number of curves needed to complete the design. We will show how a generalized lion’s stomach design can be associated with a sequence of rotations and flips of a regular polygon. Finally, we will explore how this work can be extended to mirror curves in general.

References

[1] Paulus Gerdes, Geometry From Africa: Mathematical and Educational Experiences, Mathematical Association of America, 1999.