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ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE

Year 2015, Volume: 3 Issue: 1, 103 - 114, 01.04.2015

Abstract

In this article, the hexahedron associated to metric geometry full- led by the metric of which unit sphere is hexahedron. We have analytically proved that the isometry group of the space with respect to this metric is the semi direct product of the Euclidean symmetry group of the cube and T(3) which is all translations of analytical 3􀀀space.

References

  • [1] Carrizales J. M. M. , Lopez J. L. R. , Pal U. , Yoshida M. M. and Yacaman M. J., The Completion of the Platonic Atomic Polyhedra: The Dodecahedron, Small Volume 2, Issue 3, pages 351 { 355, 2006.
  • [2] Fenn, R., Geometry, Springer Undergraduate Mathematics Series, 2003.
  • [3] Gelisgen,  O. , Kaya, R. , The Taxicab Space Group, Acta Mathematica Hungarica, Vol. 122, No.1-2, 187-200, 2009.
  • [4] Kaya, R. , Gelisgen,  O. , Ekmekci, S. , Bayar A. , Group of Isometries of CC-Plane, MJMS. , Vol. 18, No. 3 , 221-233, 2006.
  • [5] Kaya, R. , Gelisgen,  O. , Ekmekci, S. , Bayar A. , On The Group of Isometries of The Plane with Generalized Absolute Value Metric, Rocky Mountain Journal of Mathematics, Vol. 39, No. 2, 591-603, 2009.
  • [6] Lopez J. L. R, Carrizales J. M. M. and Yacaman M. J. , Low Dimensional Non - Crystallographic Metallic Nanostructures: Hrtem Simulation, Models and Experimental Results, Modern Physics Letters B. , Vol. 20, No. 13, 725-751, 2006.
  • [7] Martin, G. E. , Transformation Geometry, Springer-Verlag, 1997.
  • [8] Millman, R. S. , Parker, G.D., Geometry, A Metric Approach with Models, Undergraduate Texts in Mathematics, Springer-Verlag, 1981.
  • [9] Salihova, S., \Maksimum Metrik Geometri Uzerine", Eskisehir Osmangazi University, PhD Thesis, 2006.
  • [10] Schattschneider, D. J. , Taxicab group, Amer. Math. Monthly, 91, 423-428, 1984.
Year 2015, Volume: 3 Issue: 1, 103 - 114, 01.04.2015

Abstract

References

  • [1] Carrizales J. M. M. , Lopez J. L. R. , Pal U. , Yoshida M. M. and Yacaman M. J., The Completion of the Platonic Atomic Polyhedra: The Dodecahedron, Small Volume 2, Issue 3, pages 351 { 355, 2006.
  • [2] Fenn, R., Geometry, Springer Undergraduate Mathematics Series, 2003.
  • [3] Gelisgen,  O. , Kaya, R. , The Taxicab Space Group, Acta Mathematica Hungarica, Vol. 122, No.1-2, 187-200, 2009.
  • [4] Kaya, R. , Gelisgen,  O. , Ekmekci, S. , Bayar A. , Group of Isometries of CC-Plane, MJMS. , Vol. 18, No. 3 , 221-233, 2006.
  • [5] Kaya, R. , Gelisgen,  O. , Ekmekci, S. , Bayar A. , On The Group of Isometries of The Plane with Generalized Absolute Value Metric, Rocky Mountain Journal of Mathematics, Vol. 39, No. 2, 591-603, 2009.
  • [6] Lopez J. L. R, Carrizales J. M. M. and Yacaman M. J. , Low Dimensional Non - Crystallographic Metallic Nanostructures: Hrtem Simulation, Models and Experimental Results, Modern Physics Letters B. , Vol. 20, No. 13, 725-751, 2006.
  • [7] Martin, G. E. , Transformation Geometry, Springer-Verlag, 1997.
  • [8] Millman, R. S. , Parker, G.D., Geometry, A Metric Approach with Models, Undergraduate Texts in Mathematics, Springer-Verlag, 1981.
  • [9] Salihova, S., \Maksimum Metrik Geometri Uzerine", Eskisehir Osmangazi University, PhD Thesis, 2006.
  • [10] Schattschneider, D. J. , Taxicab group, Amer. Math. Monthly, 91, 423-428, 1984.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

T. Ermiş

R. Kaya This is me

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Ermiş, T., & Kaya, R. (2015). ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE. Konuralp Journal of Mathematics, 3(1), 103-114.
AMA Ermiş T, Kaya R. ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE. Konuralp J. Math. April 2015;3(1):103-114.
Chicago Ermiş, T., and R. Kaya. “ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 103-14.
EndNote Ermiş T, Kaya R (April 1, 2015) ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE. Konuralp Journal of Mathematics 3 1 103–114.
IEEE T. Ermiş and R. Kaya, “ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE”, Konuralp J. Math., vol. 3, no. 1, pp. 103–114, 2015.
ISNAD Ermiş, T. - Kaya, R. “ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE”. Konuralp Journal of Mathematics 3/1 (April 2015), 103-114.
JAMA Ermiş T, Kaya R. ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE. Konuralp J. Math. 2015;3:103–114.
MLA Ermiş, T. and R. Kaya. “ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 103-14.
Vancouver Ermiş T, Kaya R. ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE. Konuralp J. Math. 2015;3(1):103-14.
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