TITLE:
The Behavior of Normality when Iteratively Finding the Normal to a Line in an lp Geometry
AUTHORS:
Joshua M. Fitzhugh, David L. Farnsworth
KEYWORDS:
Minkowski Geometry; Geometric Construction; Iteration; Normality; lp Geometry; Radon Curve
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.8,
November
27,
2013
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 lp geometries with p>1repeatedly
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.