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Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space

Year 2014, Volume: 2 Issue: 3, 199 - 205, 01.12.2014

Abstract

References

  • Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • Ball, N.H., On ovals, American Mathematical Monthly, 37(7) : 348-353, 1930.
  • Barbier, E., Note sur le probléme de I’aiguille et le jeu du joint couvert, Journal de mathématiques pures et appliquées, 2(5) : 273-286, 1860.
  • Blaschke, W., Leibziger Berichte, 67 : 290, 1917.
  • Mellish, A.P., Notes on Differential Geometry, Annals of Mathematics, 32(1) : 181-190, 1931.
  • Fujiwara, M., On Space Curves of Constant Breadth, Tohoku Mathematical Journal, 5 : 180-184, 1914.
  • Hammer, P.C., Constant Breadth Curves in the Plane, Procedings of the American Mathematical Society, 6(2) : 333-334, 1955.
  • Smakal, S., Curves of Constant Breadth, Czechoslovak Mathematical Journal, 23(1) : 86-94, 1973.
  • Köse, Ö., Düzlemde Ovaller ve Sabit Genişlikli Eğrilerin Bazı Özellikleri, Doğa Bilim Dergisi, Seri B, 8(2) : 119-126, 1984.
  • Reuleaux, F., The Kinematics of Machinery, Translated by A. B. W. Kennedy, Dover Pub. New York, 1963.
  • Köse, Ö., On Space Curves of Constant Breadth, Doğa Tr. J. Math, 10(1) : 11-14, 1986.
  • Sezer, M., Differential Equations Characterizing Space Curves of Constant Breadth and a Criterion
  • for These Curves, Turkish J. of Math, 13(2) : 70-78, 1989.
  • Akdoğan, Z., and Mağden, A., Some Characterization of Curves of Constant Breadth in E Space,
  • Turk J Math, 25 : 433-444, 2001.
  • Mağden, A., and Köse, Ö., On the Curves of Constant Breadth in E Space, Tr. J. of Mathematics, 21 277-284, 1997.
  • Önder, M., Kocayiğit, H. and Candan, E., Differential Equations Characterizing Timelike and
  • Spacelike Curves of Constant Breadth in Minkowski 3-Space 1 3 866, 2011.
  • Kocayiğit, H. and Önder, M., Space Curves of Constant Breadth in Minkowski 3-Space, Annali di
  • Matematica, 192(5) : 805-814, 2013.
  • Hanson, A.J. and Ma, H., Parallel Transport Approach to Curve Framing, Indiana University,
  • Technical Report TR425, January 11, 1995.
  • Bishop, R.L., There is More Than One Way to Frame a Curve, American Mathematical Monthly, 82(3) : 246-251, 1975.
  • Hanson, A.J., and Ma, H., Quaternion Frame Approach to Streamline Visualization, IEEE
  • Transactions on Visulation and Computer Graphics, 1(2) : 164-174, 1995.
  • Bükcü, B. and Karacan, M.K., The Slant Helices according to Bishop Frame, World Academy of
  • Science, Engineering and Technology, 3(11) : 853-856, 2009.

Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space

Year 2014, Volume: 2 Issue: 3, 199 - 205, 01.12.2014

Abstract

In this paper, space curves of constant breadth according to Bishop frame in Euclidean 3-space are studied. It is shown that in some special cases, space curves of constant breadth are slant helix. Moreover, the differential equations characterizing the space curves of constant breadth in E are given. 3 are given

References

  • Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • Ball, N.H., On ovals, American Mathematical Monthly, 37(7) : 348-353, 1930.
  • Barbier, E., Note sur le probléme de I’aiguille et le jeu du joint couvert, Journal de mathématiques pures et appliquées, 2(5) : 273-286, 1860.
  • Blaschke, W., Leibziger Berichte, 67 : 290, 1917.
  • Mellish, A.P., Notes on Differential Geometry, Annals of Mathematics, 32(1) : 181-190, 1931.
  • Fujiwara, M., On Space Curves of Constant Breadth, Tohoku Mathematical Journal, 5 : 180-184, 1914.
  • Hammer, P.C., Constant Breadth Curves in the Plane, Procedings of the American Mathematical Society, 6(2) : 333-334, 1955.
  • Smakal, S., Curves of Constant Breadth, Czechoslovak Mathematical Journal, 23(1) : 86-94, 1973.
  • Köse, Ö., Düzlemde Ovaller ve Sabit Genişlikli Eğrilerin Bazı Özellikleri, Doğa Bilim Dergisi, Seri B, 8(2) : 119-126, 1984.
  • Reuleaux, F., The Kinematics of Machinery, Translated by A. B. W. Kennedy, Dover Pub. New York, 1963.
  • Köse, Ö., On Space Curves of Constant Breadth, Doğa Tr. J. Math, 10(1) : 11-14, 1986.
  • Sezer, M., Differential Equations Characterizing Space Curves of Constant Breadth and a Criterion
  • for These Curves, Turkish J. of Math, 13(2) : 70-78, 1989.
  • Akdoğan, Z., and Mağden, A., Some Characterization of Curves of Constant Breadth in E Space,
  • Turk J Math, 25 : 433-444, 2001.
  • Mağden, A., and Köse, Ö., On the Curves of Constant Breadth in E Space, Tr. J. of Mathematics, 21 277-284, 1997.
  • Önder, M., Kocayiğit, H. and Candan, E., Differential Equations Characterizing Timelike and
  • Spacelike Curves of Constant Breadth in Minkowski 3-Space 1 3 866, 2011.
  • Kocayiğit, H. and Önder, M., Space Curves of Constant Breadth in Minkowski 3-Space, Annali di
  • Matematica, 192(5) : 805-814, 2013.
  • Hanson, A.J. and Ma, H., Parallel Transport Approach to Curve Framing, Indiana University,
  • Technical Report TR425, January 11, 1995.
  • Bishop, R.L., There is More Than One Way to Frame a Curve, American Mathematical Monthly, 82(3) : 246-251, 1975.
  • Hanson, A.J., and Ma, H., Quaternion Frame Approach to Streamline Visualization, IEEE
  • Transactions on Visulation and Computer Graphics, 1(2) : 164-174, 1995.
  • Bükcü, B. and Karacan, M.K., The Slant Helices according to Bishop Frame, World Academy of
  • Science, Engineering and Technology, 3(11) : 853-856, 2009.
There are 27 citations in total.

Details

Journal Section Articles
Authors

Hüseyin Kocayiğit This is me

Muhammed Çetin This is me

Publication Date December 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 3

Cite

APA Kocayiğit, H., & Çetin, M. (2014). Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space. New Trends in Mathematical Sciences, 2(3), 199-205.
AMA Kocayiğit H, Çetin M. Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space. New Trends in Mathematical Sciences. December 2014;2(3):199-205.
Chicago Kocayiğit, Hüseyin, and Muhammed Çetin. “Space Curves of Constant Breadth According to Bishop Frame in Euclidean 3-Space”. New Trends in Mathematical Sciences 2, no. 3 (December 2014): 199-205.
EndNote Kocayiğit H, Çetin M (December 1, 2014) Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space. New Trends in Mathematical Sciences 2 3 199–205.
IEEE H. Kocayiğit and M. Çetin, “Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space”, New Trends in Mathematical Sciences, vol. 2, no. 3, pp. 199–205, 2014.
ISNAD Kocayiğit, Hüseyin - Çetin, Muhammed. “Space Curves of Constant Breadth According to Bishop Frame in Euclidean 3-Space”. New Trends in Mathematical Sciences 2/3 (December 2014), 199-205.
JAMA Kocayiğit H, Çetin M. Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space. New Trends in Mathematical Sciences. 2014;2:199–205.
MLA Kocayiğit, Hüseyin and Muhammed Çetin. “Space Curves of Constant Breadth According to Bishop Frame in Euclidean 3-Space”. New Trends in Mathematical Sciences, vol. 2, no. 3, 2014, pp. 199-05.
Vancouver Kocayiğit H, Çetin M. Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space. New Trends in Mathematical Sciences. 2014;2(3):199-205.