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The Behavior of Normality when Iteratively Finding the Normal to a Line in an <sub>lp</sub> Geometry
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
- 1 School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
- 2 School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
Advances in Pure Mathematics·Volume 03 (2013)·Pages 647–652·Published 27 November 2013·DOI10.4236/apm.2013.38086
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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.
KeywordsMinkowski GeometryGeometric ConstructionIterationNormality<sub>lp</sub>GeometryRadon Curve
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