The Behavior of Normality when Iteratively Finding the Normal to a Line in an _lp Geometry

Joshua M. Fitzhugh, David L. Farnsworth

School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA.

DOI: 10.4236/apm.2013.38086                

Abstract

The normal direction to the normal direction to a line in Minkowski geometries generally does not give the original line. We show that in l_p geometries with p>1 repeatedly finding the normal line through the origin gives sequences of lines that monotonically approach specific lines of symmetry of the unit circle. Which lines of symmetry that are approached depends upon the value of p and the slope of the initial line.

Keywords

Minkowski Geometry; Geometric Construction; Iteration; Normality; _lp Geometry; Radon Curve

Conflicts of Interest

The authors declare no conflicts of interest.

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