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 > 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.
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J. Fitzhugh and D. Farnsworth, "The Behavior of Normality when Iteratively Finding the Normal to a Line in an lp Geometry," Advances in Pure Mathematics, Vol. 3 No. 8, 2013, pp. 647-652. doi: 10.4236/apm.2013.38086.
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