Article citationsMore>>

R. V. Benson, “Euclidean Geometry and Convexity,” McGraw-Hill, New York, 1966.

has been cited by the following article:

• 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.