The Relationship of the Cotangent Function to Special Relativity Theory, Silver Means, p-cycles, and Chaos Theory

Jay Kappraff¹* and Gary W. Adamson²

¹New Jersey Institute of Technology, Newark, NJ 07102, U.S.A.
²P.O. Box 124571, San Diego, CA 92112-4571, U.S.A.
*E-mail address: kappraff@aol.com

(Received October 14, 2003; Accepted November 28, 2003)

Keywords: Cotangent, Relativity, Silver Means, Periodic Trajectories, Chaos Theory

Abstract. The cotangent function is shown to play a key role in special relativity theory, silver mean constants, p-cycles for all positive integer values of p, and period doubling bifurcations from chaos theory. Geometry and properties of number play important roles in the analysis. A new theorem pertaining to periodic continued fractions is introduced.