Edge, Micah Symmetry in Fibonacci numbers. (English) Zbl 1274.11038 Symmetry Cult. Sci. 20, No. 1-4, 393-408 (2009). Summary: This article outlines a number of observations regarding Fibonacci numbers as they relate to symmetry. The connection between Fibonacci numbers and symmetry uncovered a symmetrical organization of Fibonacci numbers called Fibonacci system. Exploration of the Fibonacci system uncovered a relationship between Fibonacci numbers and circle patterns that were related via motion and rotation to Fibonacci system numbers. When the concept of motion and rotation is applied to the Fibonacci system it creates Fibonacci numbers, the golden ratio, and concentric circle patterns as well as reveals a pivot point used for the self replication of the circle system. The circle patterns created through the processes described in this paper were found to align with the rhythms of ratios on a multitude of natural objects. MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 00A69 General applied mathematics Keywords:Fibonacci; symmetry; Fibonacci cystem; rhythm; motion; circle cystem; circle map; concentric; orbital and pivotal PDFBibTeX XMLCite \textit{M. Edge}, Symmetry Cult. Sci. 20, No. 1--4, 393--408 (2009; Zbl 1274.11038)