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THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY

Year 2011, Volume: 4 Issue: 2, 193 - 207, 30.10.2011

Kevin P. Thompson

Abstract

 While the concept of straight-line length is well understood intaxicab geometry, little research has been done into the length of curves or the nature of area and volume in this geometry. This paper sets forth a comprehensive view of the basic dimensional measures in taxicab geometry.

Keywords

taxicab geometry distance integration arc length area volume

References

  • [1] Akça, Ziya and Rüstem Kaya. On the Distance Formulae in Three Dimensional Taxicab Space, Hadronic Journal, Vol. 27, No. 5 (2004), pp. 521-532.
  • [2] Çolakoğlu, H. Baris and Rüstem Kaya. Volume of a Tetrahedron in the Taxicab Space, Mis- souri Journal of Mathematical Sciences, Vol. 21, No. 1 (Winter 2009), pp. 21-27.
  • [3] Euler, Russell and Jawad Sadek. The πs Go Full Circle, Mathematics Magazine, Vol. 72, No. 1 (Feb 1999), pp. 59-63.
  • [4] Janssen, Christina. Taxicab Geometry: Not the Shortest Ride Around Town, dissertation (unpublished), Iowa State University, Jul 2007.
  • [5] Kaya, Rüstem. Area Formula for Taxicab Triangles, Pi Mu Epsilon Journal, Vol. 12, No. 4 (Spring 2006), pp. 219-220.
  • [6] Kaya, Rüstem; Ziya Akça; I. Ginalti; and Minevver Özcan, General Equation for Taxicab Conics and Their Classification, Mitt. Math. Ges. Hamburg, Vol. 19 (2000), pp. 135-148.
  • [7] Krause, Eugene F. “Taxicab Geometry: An Adventure in Non-Euclidean Geometry”, Dover, New York, 1986.
  • [8] Laatsch, Richard. Pyramidal Sections in Taxicab Geometry, Mathematics Magazine, Vol. 55, No. 4 (Sep 1982), pp. 205-212.
  • [9] Özcan, Münevver; Süheyla Ekmekçi; and Ayse Bayar. A Note on the Variation of Taxicab Lengths Under Rotations, Pi Mu Epsilon Journal, Vol. 11, No. 7 (Fall 2002), pp. 381-384.
  • [10] Özcan, Münevver and Rüstem Kaya. On the Ratio of Directed Lengths in the Taxicab Plane and Related Properties, Missouri Journal of Mathematical Sciences, Vol. 14, No. 2 (Spring 2002).
  • [11] Özcan, Münevver and Rüstem Kaya. Area of a Taxicab Triangle in Terms of the Taxicab Distance, Missouri Journal of Mathematical Sciences, Vol. 15, No. 3 (Fall 2003), pp. 21-27.
  • [12] Thompson, Kevin and Tevian Dray. Taxicab Angles and Trigonometry, The Pi Mu Epsilon Journal, Vol. 11, No. 2 (Spring 2000), pp. 87-96.

Year 2011, Volume: 4 Issue: 2, 193 - 207, 30.10.2011

Kevin P. Thompson

Abstract

References

  • [1] Akça, Ziya and Rüstem Kaya. On the Distance Formulae in Three Dimensional Taxicab Space, Hadronic Journal, Vol. 27, No. 5 (2004), pp. 521-532.
  • [2] Çolakoğlu, H. Baris and Rüstem Kaya. Volume of a Tetrahedron in the Taxicab Space, Mis- souri Journal of Mathematical Sciences, Vol. 21, No. 1 (Winter 2009), pp. 21-27.
  • [3] Euler, Russell and Jawad Sadek. The πs Go Full Circle, Mathematics Magazine, Vol. 72, No. 1 (Feb 1999), pp. 59-63.
  • [4] Janssen, Christina. Taxicab Geometry: Not the Shortest Ride Around Town, dissertation (unpublished), Iowa State University, Jul 2007.
  • [5] Kaya, Rüstem. Area Formula for Taxicab Triangles, Pi Mu Epsilon Journal, Vol. 12, No. 4 (Spring 2006), pp. 219-220.
  • [6] Kaya, Rüstem; Ziya Akça; I. Ginalti; and Minevver Özcan, General Equation for Taxicab Conics and Their Classification, Mitt. Math. Ges. Hamburg, Vol. 19 (2000), pp. 135-148.
  • [7] Krause, Eugene F. “Taxicab Geometry: An Adventure in Non-Euclidean Geometry”, Dover, New York, 1986.
  • [8] Laatsch, Richard. Pyramidal Sections in Taxicab Geometry, Mathematics Magazine, Vol. 55, No. 4 (Sep 1982), pp. 205-212.
  • [9] Özcan, Münevver; Süheyla Ekmekçi; and Ayse Bayar. A Note on the Variation of Taxicab Lengths Under Rotations, Pi Mu Epsilon Journal, Vol. 11, No. 7 (Fall 2002), pp. 381-384.
  • [10] Özcan, Münevver and Rüstem Kaya. On the Ratio of Directed Lengths in the Taxicab Plane and Related Properties, Missouri Journal of Mathematical Sciences, Vol. 14, No. 2 (Spring 2002).
  • [11] Özcan, Münevver and Rüstem Kaya. Area of a Taxicab Triangle in Terms of the Taxicab Distance, Missouri Journal of Mathematical Sciences, Vol. 15, No. 3 (Fall 2003), pp. 21-27.
  • [12] Thompson, Kevin and Tevian Dray. Taxicab Angles and Trigonometry, The Pi Mu Epsilon Journal, Vol. 11, No. 2 (Spring 2000), pp. 87-96.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Kevin P. Thompson This is me

Publication Date October 30, 2011
Published in Issue Year 2011 Volume: 4 Issue: 2

Cite

APA Thompson, K. P. (2011). THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY. International Electronic Journal of Geometry, 4(2), 193-207.
AMA Thompson KP. THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY. Int. Electron. J. Geom. October 2011;4(2):193-207.
Chicago Thompson, Kevin P. “THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY”. International Electronic Journal of Geometry 4, no. 2 (October 2011): 193-207.
EndNote Thompson KP (October 1, 2011) THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY. International Electronic Journal of Geometry 4 2 193–207.
IEEE K. P. Thompson, “THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY”, Int. Electron. J. Geom., vol. 4, no. 2, pp. 193–207, 2011.
ISNAD Thompson, Kevin P. “THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY”. International Electronic Journal of Geometry 4/2 (October 2011), 193-207.
JAMA Thompson KP. THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY. Int. Electron. J. Geom. 2011;4:193–207.
MLA Thompson, Kevin P. “THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY”. International Electronic Journal of Geometry, vol. 4, no. 2, 2011, pp. 193-07.
Vancouver Thompson KP. THE NATURE OF LENGTH, AREA, AND VOLUME IN TAXICAB GEOMETRY. Int. Electron. J. Geom. 2011;4(2):193-207.