Research Article
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The Alpha Distance Formulae

Year 2024, Volume: 5 Issue: 2, 60 - 71, 31.07.2024
https://doi.org/10.54974/fcmathsci.1312895

Abstract

In this study, we define the concept of tangent in two and three-dimensional alpha spaces concerning the alpha circles and the alpha spheres. Then using this concept, we derive the alpha distance formulae between points, a point and a line, between two lines and a point and a plane of the alpha spaces. Finally, we give simple area and volume formulas in the three dimensional space in terms of the alpha distances.

References

  • Akça Z., Kaya R., On the distance formulae in three dimensional taxicab space, Hadronic Journal, 27, 521-532, 2004.
  • Chen G., Lines and Circles in Taxicab Geometry, M. Sc., Central Missouri State University, Missouri, USA, 1992.
  • Çolakoğlu H.B., Concerning the alpha distance, Algebras, Groups, and Geometries, 8, 1-14, 2011.
  • Çolakoğlu H.B., On the distance formulae in the generalized taxicab geometry, Turkish Journal of Mathematics, 43, 1578-1594, 2019.
  • Çolakoğlu H.B., A generalization of the Minkowski distance and new definitions of the central conics, Turkish Journal of Mathematics, 44, 319-330, 2020.
  • Çolakoğlu H.B., Gelişgen Ö., Kaya R., Area formulas for a triangle in the alpha plane, Mathematical Communications, 18, 123-132, 2013.
  • Çolakoğlu H.B., Gelişgen Ö., Kaya R., Pythagorean theorems in the alpha plane, Mathematical Communications, 14, 211-221, 2009.
  • Deza M.M., Deza E., Encyclopedia of Distances, Springer, 2009.
  • Gelişgen Ö., Ermiş T., Inversions and fractal patterns in alpha plane, International Electronic Journal of Geometry, 16(1), 398-411, 2023.
  • Gelişgen Ö., Kaya R., Özcan M., Distance formulae in the Chinese checker space, International Journal of Pure and Applied Mathematics, 26, 35-44, 2006.
  • Gelişgen Ö., Kaya R., On α-distance in three dimensional space, APPS Applied Sciences, 8, 65-69, 2006.
  • Gelişgen Ö., Kaya R., Generalization of α-distance to n-dimensional space, Croatian Society for Geometry and Graphics, 10, 33-35, 2006.
  • Krause E.F., Taxicab Geometry, Dover, 1986.
  • Menger K., You Will Like Geometry, A Guide Book for the Illinois Institute of Technology Geometry Exhibition, Museum of Science and Industry, 1961.
  • Tian S., Alpha-distance - A generalization of Chinese checker distance and taxicab distance, Missouri Journal of Mathematical Sciences, 17, 35-40, 2005.
  • Wallen L.J., Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal, 26, 178-190, 1995.
Year 2024, Volume: 5 Issue: 2, 60 - 71, 31.07.2024
https://doi.org/10.54974/fcmathsci.1312895

Abstract

References

  • Akça Z., Kaya R., On the distance formulae in three dimensional taxicab space, Hadronic Journal, 27, 521-532, 2004.
  • Chen G., Lines and Circles in Taxicab Geometry, M. Sc., Central Missouri State University, Missouri, USA, 1992.
  • Çolakoğlu H.B., Concerning the alpha distance, Algebras, Groups, and Geometries, 8, 1-14, 2011.
  • Çolakoğlu H.B., On the distance formulae in the generalized taxicab geometry, Turkish Journal of Mathematics, 43, 1578-1594, 2019.
  • Çolakoğlu H.B., A generalization of the Minkowski distance and new definitions of the central conics, Turkish Journal of Mathematics, 44, 319-330, 2020.
  • Çolakoğlu H.B., Gelişgen Ö., Kaya R., Area formulas for a triangle in the alpha plane, Mathematical Communications, 18, 123-132, 2013.
  • Çolakoğlu H.B., Gelişgen Ö., Kaya R., Pythagorean theorems in the alpha plane, Mathematical Communications, 14, 211-221, 2009.
  • Deza M.M., Deza E., Encyclopedia of Distances, Springer, 2009.
  • Gelişgen Ö., Ermiş T., Inversions and fractal patterns in alpha plane, International Electronic Journal of Geometry, 16(1), 398-411, 2023.
  • Gelişgen Ö., Kaya R., Özcan M., Distance formulae in the Chinese checker space, International Journal of Pure and Applied Mathematics, 26, 35-44, 2006.
  • Gelişgen Ö., Kaya R., On α-distance in three dimensional space, APPS Applied Sciences, 8, 65-69, 2006.
  • Gelişgen Ö., Kaya R., Generalization of α-distance to n-dimensional space, Croatian Society for Geometry and Graphics, 10, 33-35, 2006.
  • Krause E.F., Taxicab Geometry, Dover, 1986.
  • Menger K., You Will Like Geometry, A Guide Book for the Illinois Institute of Technology Geometry Exhibition, Museum of Science and Industry, 1961.
  • Tian S., Alpha-distance - A generalization of Chinese checker distance and taxicab distance, Missouri Journal of Mathematical Sciences, 17, 35-40, 2005.
  • Wallen L.J., Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal, 26, 178-190, 1995.
There are 16 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Articles
Authors

Harun Barış Çolakoğlu 0000-0001-5559-9768

Publication Date July 31, 2024
Published in Issue Year 2024 Volume: 5 Issue: 2

Cite

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.