The Behavior of Normality when Iteratively Finding the Normal to a Line in an _{lp} Geometry

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

KEYWORDS

Minkowski Geometry; Geometric Construction; Iteration; Normality;_{lp} Geometry; Radon Curve

Minkowski Geometry; Geometric Construction; Iteration; Normality;

Cite this paper

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.

J. Fitzhugh and D. Farnsworth, "The Behavior of Normality when Iteratively Finding the Normal to a Line in an

References

[1] A. C. Thompson, “Minkowski Geometry,” Cambridge University Press, Cambridge, 1996.

http://dx.doi.org/10.1017/CBO9781107325845

[2] E. F. Krause, “Taxicab Geometry,” Dover Publications, New York, 1986.

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

[4] B. V. Dekster, “An Angle in Minkowski Space,” Journal of Geometry, Vol. 80, No. 1, 2004, pp. 31-47.

[5] G. J. Ruane and G. A. Swartzlander Jr., “Optical Vortex Coronagraphy with an Elliptical Aperture,” Applied Optics, Vol. 52, No. 2, 2013, pp. 171-176.

http://dx.doi.org/10.1364/AO.52.000171

[6] M. Gardner, “Mathematical Carnival,” Alfred A. Knopf, New York, 1975.

[7] J. C. álvarez Paiva and A. Thompson, “On the Perimeter and Area of the Unit Disc,” The American Mathematical Monthly, Vol. 112, No. 2, 2005, pp. 141-154.

http://dx.doi.org/10.2307/30037412

[8] J. J. Schaffer, “The Self-Circumferences of Polar Convex Disks,” Archiv de Mathematik, Vol. 24, 1973, pp. 87-90.

http://dx.doi.org/10.1007/BF01228179

[9] J. B. Keller and R. Vakil, “pp, the Value of p in lp,” The American Mathematical Monthly, Vol. 116, No. 10, 2009, pp. 931-935.

http://dx.doi.org/10.4169/000298909X477069

[10] J. Radon, “über eine Besondere Art Ebener Konvexer Kurven,” Berichte der Sachsische Akademie der Wissenschaften zu Leipzig, Vol. 68, 1916, pp. 131-134.

[1] A. C. Thompson, “Minkowski Geometry,” Cambridge University Press, Cambridge, 1996.

http://dx.doi.org/10.1017/CBO9781107325845

[2] E. F. Krause, “Taxicab Geometry,” Dover Publications, New York, 1986.

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

[4] B. V. Dekster, “An Angle in Minkowski Space,” Journal of Geometry, Vol. 80, No. 1, 2004, pp. 31-47.

[5] G. J. Ruane and G. A. Swartzlander Jr., “Optical Vortex Coronagraphy with an Elliptical Aperture,” Applied Optics, Vol. 52, No. 2, 2013, pp. 171-176.

http://dx.doi.org/10.1364/AO.52.000171

[6] M. Gardner, “Mathematical Carnival,” Alfred A. Knopf, New York, 1975.

[7] J. C. álvarez Paiva and A. Thompson, “On the Perimeter and Area of the Unit Disc,” The American Mathematical Monthly, Vol. 112, No. 2, 2005, pp. 141-154.

http://dx.doi.org/10.2307/30037412

[8] J. J. Schaffer, “The Self-Circumferences of Polar Convex Disks,” Archiv de Mathematik, Vol. 24, 1973, pp. 87-90.

http://dx.doi.org/10.1007/BF01228179

[9] J. B. Keller and R. Vakil, “pp, the Value of p in lp,” The American Mathematical Monthly, Vol. 116, No. 10, 2009, pp. 931-935.

http://dx.doi.org/10.4169/000298909X477069

[10] J. Radon, “über eine Besondere Art Ebener Konvexer Kurven,” Berichte der Sachsische Akademie der Wissenschaften zu Leipzig, Vol. 68, 1916, pp. 131-134.