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Üç Boyutlu Tetrakis Hexahedron Uzayında Küresel İnversiyonlar Üzerine

Year 2022, Volume: 38 Issue: 1, 100 - 108, 30.04.2022

Zeynep Can

Abstract

Bu çalışmada, Tetrakis Hexahedron uzayında küresel inversiyonların genel özellikleri ve temel kavramları üzerinde çalıştık. Ayrıca çifte oran ve harmonik eşlenik kavramları ile R_TH^3 de bir Tetrakis Hexahedron küresine göre bir inversiyon altında doğruların, düzlemlerin ve Tetrakis Hexahedron kürelerinin küresel tersleri araştırıldı.

Keywords

Tetrakis Hexahedron Uzayı Tetrakis Hexahedron Küresi Çifte Oran Harmonik Bölme Küresel İnversiyon

References

  • Referans 1 Patterson B.C., The origins of the Geometric Principle of Inversion,Isis, 19-(1), (1933), 154 - 180.
  • Referans 2 Ramirez, J.L., Rubiano G.N., Jurcic-Zlobec, B., 2015. Generating Fractal Patterns by Using p-circle Inversion, Fractals, 23-(4), 1-13.
  • Referans 3 N. Childress, 1964. Inversion with respect to the central conics, Math. Mag., 38-(3), 147-149.
  • Referans 4 Nickel, J. A., 1995. A Budget of inversion, Math. Comput. Modelling, 21, 87-93.
  • Referans 5 Ramirez, J.L., 2014. Inversions in an ellipse, Forum Geom., 14, 107-115.
  • Referans 6 Gdawiec, K., 2014, Star-shaped Set Inversion Fractals, Fractals, 22-(4), 1-7.
  • Referans 7 Ramirez, J.L. and Rubiano, G.N., 2014. A Geometrical Construction of Inverse Points with Respect to an Ellipse, nternational Journal of Mathematical Education in Science and Technology, 45-(8), 1254-1259.
  • Referans 8 Ramirez, J.L and Rubiano, G.N., 2014. Elliptic Inversion of Two Dimensional Objects, International Journal of Geometry, 3-(1), 12-27.
  • Referans 9 Pekzorlu, A., 2019. On Inversions in Non-Euclidean Geometries, Phd. Thesis, Eskişehir Osmangazi University, 106p, Eskişehir.
  • Referans 10 Bayar, A. and Ekmekçi, S. , 2014. On circular inversions in taxicab plane, Journal of Advanced Research in Pure Mathematics., 6-(4), 33-39.
  • Referans 11 Gelişgen, Ö. and Ermiş, T., 2019. Some Properties of Inversions in Alpha Plane, Forum Geometricorum, 19, 1-9.
  • Referans 12 Ramirez, J.L. and Rubiano, G.N., 2016. A Generalization of the Spherical Inversion, International Journal of Mathematical Education in Science and Technology, 48-(1), 132-149.
  • Referans 13 Pekzorlu, A. and Bayar, A., 2020. On the Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space, Com. Fac. of Sci. Univ. of Ank. Ser. A1 Math. and Stat., 69-(2), 1498-1507.
  • Referans 14 Pekzorlu, A. and Bayar, A., 2020. Taxicab Spherical Inversions in Taxicab Space, Journal of Mahani Math. Research Center, Vol. 9, no 1-2, 45-54.
  • Referans 15 Thompson, A. C., 1996. Minkowski Geometry, Cambridge University Press, 346p.
  • Referans 16 Cromwell, P. R., 1997. Polyhedra, Cambridge University Press, 443p.
  • Referans 17 Ermiş, T., 2014. On The Relations Between The Metric Geometries and Regular Polyhedra, Phd.Thesis, Eskisehir Osmangazi University, 93p, Eskişehir.
  • Referans 18 Gelişgen, Ö. and Kaya, R., 2019. The Taxicab Space Group, Acta Mathematica Hungarica, 122(1-2), 187– 200.
  • Referans 19 Gelişgen, Ö. and Kaya, R., 2015. The Isometry Group of Chinese Checker Space, International Electronic Journal of Geometry, 8-(2), 82–96.
  • Referans 20 Can, Z., Gelişgen, Ö., Kaya, R., 2015. On the Metrics Induced by Icosidodecahedron and Rhombic Triacontahedron, Scientific and Professional Journal of the Croatian Society for Geometry and Graphics (KoG), 19, 17-23.
  • Referans 21 Can, Z., Çolak, Z., Gelişgen, Ö., 2015. A Note On The Metrics Induced By Triakis Icosahedron And Disdyakis Triacontahedron, Eurasian Academy of Sciences Eurasian Life Sciences Journal, 1, 1- 11.
  • Referans 22 Çolak Z. and Gelişgen Ö., 2015. New Metrics For Deltoidal Hexacontahedron and Pentakis Dodecahedron, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 19(3), 353-360.
  • Referans 23 Gelişgen, Ö. and Çolak, Z., 2015. A Family of Metrics for Some Polyhedra, Automation Computers Applied Mathematics Scientific Journal, 24-(1), 3–15.
  • Referans 24 Gelişgen, Ö. and Can, Z., 2016. On The Family of Metrics for Some Platonic and Archimedean Polyhedra, Konuralp Journal of Mathematics, 4, 25-33.
  • Referans 25 Gelişgen, Ö., Ermiş, T., Günaltılı, İ., 2017. A Note About The Metrics Induced by Truncated Dodecahedron And Truncated Icosahedron, International Journal Of Geometry, 2(6), 5 – 16.
  • Referans 26 Ermiş, T, Savcı., Ü. Z., Gelişgen, Ö., 2019. A Note About Truncated Rhombicuboctahedron and Truncated Rhombicicosidodecahedron Space, Scientific Studies and Research Series Mathematics and Informatics, 29-(1), 73–88.
  • Referans 27 Savcı, Ü. Z., 2019. Truncated Truncated Dodecahedron and Truncated Truncated Icosahedron Spaces, Cumhuriyet Science Journal (CSJ), 40-(2), 457-470.
  • Referans 28 Blair, D., 2000. Inversion Theory and Conformal Mapping, Student Mathematical Library, American Mathematical Society, 118p.
  • Referans 29 Özcan, M. and Kaya, R., 2002. On the ratio of directed lengths in the Taxicab plane and related properties, Missouri J. of Math. Sci., 14, 107-117.

On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space

Year 2022, Volume: 38 Issue: 1, 100 - 108, 30.04.2022

Zeynep Can

Abstract

In this research, we study on general properties and basic concepts of spherical inversions in Tetrakis Hexahedron space. We also investigate cross ratio and harmonic conjugates and inverses of lines, planes and Tetrakis Hexahedron spheres in R_TH^3 under an inversion with respect to a Tetrakis Hexahedron sphere.

Keywords

Tetrakis Hexahedron Space Tetrakis Hexahedron Sphere Cross Ratio Harmonic Conjugates Spherical Inversion

References

  • Referans 1 Patterson B.C., The origins of the Geometric Principle of Inversion,Isis, 19-(1), (1933), 154 - 180.
  • Referans 2 Ramirez, J.L., Rubiano G.N., Jurcic-Zlobec, B., 2015. Generating Fractal Patterns by Using p-circle Inversion, Fractals, 23-(4), 1-13.
  • Referans 3 N. Childress, 1964. Inversion with respect to the central conics, Math. Mag., 38-(3), 147-149.
  • Referans 4 Nickel, J. A., 1995. A Budget of inversion, Math. Comput. Modelling, 21, 87-93.
  • Referans 5 Ramirez, J.L., 2014. Inversions in an ellipse, Forum Geom., 14, 107-115.
  • Referans 6 Gdawiec, K., 2014, Star-shaped Set Inversion Fractals, Fractals, 22-(4), 1-7.
  • Referans 7 Ramirez, J.L. and Rubiano, G.N., 2014. A Geometrical Construction of Inverse Points with Respect to an Ellipse, nternational Journal of Mathematical Education in Science and Technology, 45-(8), 1254-1259.
  • Referans 8 Ramirez, J.L and Rubiano, G.N., 2014. Elliptic Inversion of Two Dimensional Objects, International Journal of Geometry, 3-(1), 12-27.
  • Referans 9 Pekzorlu, A., 2019. On Inversions in Non-Euclidean Geometries, Phd. Thesis, Eskişehir Osmangazi University, 106p, Eskişehir.
  • Referans 10 Bayar, A. and Ekmekçi, S. , 2014. On circular inversions in taxicab plane, Journal of Advanced Research in Pure Mathematics., 6-(4), 33-39.
  • Referans 11 Gelişgen, Ö. and Ermiş, T., 2019. Some Properties of Inversions in Alpha Plane, Forum Geometricorum, 19, 1-9.
  • Referans 12 Ramirez, J.L. and Rubiano, G.N., 2016. A Generalization of the Spherical Inversion, International Journal of Mathematical Education in Science and Technology, 48-(1), 132-149.
  • Referans 13 Pekzorlu, A. and Bayar, A., 2020. On the Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space, Com. Fac. of Sci. Univ. of Ank. Ser. A1 Math. and Stat., 69-(2), 1498-1507.
  • Referans 14 Pekzorlu, A. and Bayar, A., 2020. Taxicab Spherical Inversions in Taxicab Space, Journal of Mahani Math. Research Center, Vol. 9, no 1-2, 45-54.
  • Referans 15 Thompson, A. C., 1996. Minkowski Geometry, Cambridge University Press, 346p.
  • Referans 16 Cromwell, P. R., 1997. Polyhedra, Cambridge University Press, 443p.
  • Referans 17 Ermiş, T., 2014. On The Relations Between The Metric Geometries and Regular Polyhedra, Phd.Thesis, Eskisehir Osmangazi University, 93p, Eskişehir.
  • Referans 18 Gelişgen, Ö. and Kaya, R., 2019. The Taxicab Space Group, Acta Mathematica Hungarica, 122(1-2), 187– 200.
  • Referans 19 Gelişgen, Ö. and Kaya, R., 2015. The Isometry Group of Chinese Checker Space, International Electronic Journal of Geometry, 8-(2), 82–96.
  • Referans 20 Can, Z., Gelişgen, Ö., Kaya, R., 2015. On the Metrics Induced by Icosidodecahedron and Rhombic Triacontahedron, Scientific and Professional Journal of the Croatian Society for Geometry and Graphics (KoG), 19, 17-23.
  • Referans 21 Can, Z., Çolak, Z., Gelişgen, Ö., 2015. A Note On The Metrics Induced By Triakis Icosahedron And Disdyakis Triacontahedron, Eurasian Academy of Sciences Eurasian Life Sciences Journal, 1, 1- 11.
  • Referans 22 Çolak Z. and Gelişgen Ö., 2015. New Metrics For Deltoidal Hexacontahedron and Pentakis Dodecahedron, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 19(3), 353-360.
  • Referans 23 Gelişgen, Ö. and Çolak, Z., 2015. A Family of Metrics for Some Polyhedra, Automation Computers Applied Mathematics Scientific Journal, 24-(1), 3–15.
  • Referans 24 Gelişgen, Ö. and Can, Z., 2016. On The Family of Metrics for Some Platonic and Archimedean Polyhedra, Konuralp Journal of Mathematics, 4, 25-33.
  • Referans 25 Gelişgen, Ö., Ermiş, T., Günaltılı, İ., 2017. A Note About The Metrics Induced by Truncated Dodecahedron And Truncated Icosahedron, International Journal Of Geometry, 2(6), 5 – 16.
  • Referans 26 Ermiş, T, Savcı., Ü. Z., Gelişgen, Ö., 2019. A Note About Truncated Rhombicuboctahedron and Truncated Rhombicicosidodecahedron Space, Scientific Studies and Research Series Mathematics and Informatics, 29-(1), 73–88.
  • Referans 27 Savcı, Ü. Z., 2019. Truncated Truncated Dodecahedron and Truncated Truncated Icosahedron Spaces, Cumhuriyet Science Journal (CSJ), 40-(2), 457-470.
  • Referans 28 Blair, D., 2000. Inversion Theory and Conformal Mapping, Student Mathematical Library, American Mathematical Society, 118p.
  • Referans 29 Özcan, M. and Kaya, R., 2002. On the ratio of directed lengths in the Taxicab plane and related properties, Missouri J. of Math. Sci., 14, 107-117.
There are 29 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Zeynep Can 0000-0003-2656-5555

Early Pub Date April 30, 2022
Publication Date April 30, 2022
Published in Issue Year 2022 Volume: 38 Issue: 1

Cite

APA Can, Z. (2022). On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 38(1), 100-108.
AMA Can Z. On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. April 2022;38(1):100-108.
Chicago Can, Zeynep. “On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 38, no. 1 (April 2022): 100-108.
EndNote Can Z (April 1, 2022) On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 38 1 100–108.
IEEE Z. Can, “On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space”, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, vol. 38, no. 1, pp. 100–108, 2022.
ISNAD Can, Zeynep. “On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 38/1 (April 2022), 100-108.
JAMA Can Z. On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. 2022;38:100–108.
MLA Can, Zeynep. “On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, vol. 38, no. 1, 2022, pp. 100-8.
Vancouver Can Z. On Spherical Inversions in Three Dimensional Tetrakis Hexahedron Space. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. 2022;38(1):100-8.
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