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Yıl 2015, Cilt: 3 Sayı: 2, 27 - 33, 30.10.2015

S. Ekmekçi Z. Akça K. Altıntaş

https://doi.org/10.36753/mathenot.421326
Cited By: 1

Öz

Kaynakça

  • [1] Akça, Z., Bayar, A. and Ekmekçi, S., The norm in CC-plane geometry. Pi Mu Epsilon J. 12 (2007), no. 6, 321-324 .
  • [2] Akça, Z. and Kaya, R., On Taxicab Trigonometry. Jour. of Inst. of Math & Comp. Sci. (Math. Ser.) 10 (1997), no. 3, 151-159 .
  • [3] Altıntaş, A.K., Oklidyen Düzlemdeki Bazı Geometrik Problemlerin Genelleştirilmiş Taksi Metrikli Geometriye Uygulaması. Eskişehir Osmangazi Universitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 2009.
  • [4] Bayar, A., On Trigonometric Functions in Maximum Metric. Kog 12 (2008), 45-48 .
  • [5] Bayar, A. , Ekmekçi, S., Özcan, M., On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane. International Electronic Journal Of Geometry 2 (2009), no. 1, 17-24 .
  • [6] Bayar, A., Ekmekçi, S. and Akça, Z., On the plane geometry with generalized absolute value metric. Mathematical Problems in Engineering Vol.2008, Article ID 673275, 8 pages.
  • [7] Bayar, A. and Ekmekçi, S., On the Chinese-Checker Sine And Cosine Functions. International Journal of Mathematics and Analysis 1 (2006), no. 3, 249-259 .
  • [8] Brisbin, R. and Artola, P., Taxicab Trigonometry. Pi Mu Epsilon J. 8 (1985), no. 2, 89-95 .
  • [9] Ekmekçi, S., Bayar, A., Altıntaş, A. K., On the Group of Isometries of the Generalized Taxicab Plane. International Journal of Comtemporary Mathematical Sciences 10 (2015), no. 4, 159-166 .
  • [10] Krause, E.F., Taxicab Geometry, Addison - Wesley Publishing Company, Menlo Park, CA (1975).
  • [11] Menger, K.,You Will Like Geometry, Guidebook of the Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • [12] Özcan, M., Ekmek¸ci, S. and Bayar, A., A Note on the Variation of the Taxicab Lengths Under Rotations. Pi Mu Epsilon J. 11 (2002), no. 7, 381-384 .
  • [13] Thompson, K. and Dray, T., Taxicab Angles and Trigonometry. Pi Mu Epsilon J. 11 (2000), no. 2, 87-97 .
  • [14] Wallen, L. J., Kepler, The Taxicab Metric, and Beyond: An isoperimetric Primer. The College Mathematics Journal 26 (1995), no. 3, 178-190.

ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC

Yıl 2015, Cilt: 3 Sayı: 2, 27 - 33, 30.10.2015

S. Ekmekçi Z. Akça K. Altıntaş

https://doi.org/10.36753/mathenot.421326
Cited By: 1

Öz

In this paper, the plane with the generalized taxicab metric is

considered and the trigonometric functions and the norm are de ned. Then,

the cosine and the sine functions are developed by using the reference angle

with respect to the generalized taxicab metric. It is shown that Schwarz's

inequality is valid under restricted case of d_Tg -metric. Finally, the area of

any triangle in the plane with the generalized taxicab metric is given as the

geometrical interpretation that contains the trigonometric functions and norm.

Anahtar Kelimeler

trigonometric functions non- Euclidean metric generalized taxicab metric

Kaynakça

  • [1] Akça, Z., Bayar, A. and Ekmekçi, S., The norm in CC-plane geometry. Pi Mu Epsilon J. 12 (2007), no. 6, 321-324 .
  • [2] Akça, Z. and Kaya, R., On Taxicab Trigonometry. Jour. of Inst. of Math & Comp. Sci. (Math. Ser.) 10 (1997), no. 3, 151-159 .
  • [3] Altıntaş, A.K., Oklidyen Düzlemdeki Bazı Geometrik Problemlerin Genelleştirilmiş Taksi Metrikli Geometriye Uygulaması. Eskişehir Osmangazi Universitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 2009.
  • [4] Bayar, A., On Trigonometric Functions in Maximum Metric. Kog 12 (2008), 45-48 .
  • [5] Bayar, A. , Ekmekçi, S., Özcan, M., On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane. International Electronic Journal Of Geometry 2 (2009), no. 1, 17-24 .
  • [6] Bayar, A., Ekmekçi, S. and Akça, Z., On the plane geometry with generalized absolute value metric. Mathematical Problems in Engineering Vol.2008, Article ID 673275, 8 pages.
  • [7] Bayar, A. and Ekmekçi, S., On the Chinese-Checker Sine And Cosine Functions. International Journal of Mathematics and Analysis 1 (2006), no. 3, 249-259 .
  • [8] Brisbin, R. and Artola, P., Taxicab Trigonometry. Pi Mu Epsilon J. 8 (1985), no. 2, 89-95 .
  • [9] Ekmekçi, S., Bayar, A., Altıntaş, A. K., On the Group of Isometries of the Generalized Taxicab Plane. International Journal of Comtemporary Mathematical Sciences 10 (2015), no. 4, 159-166 .
  • [10] Krause, E.F., Taxicab Geometry, Addison - Wesley Publishing Company, Menlo Park, CA (1975).
  • [11] Menger, K.,You Will Like Geometry, Guidebook of the Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • [12] Özcan, M., Ekmek¸ci, S. and Bayar, A., A Note on the Variation of the Taxicab Lengths Under Rotations. Pi Mu Epsilon J. 11 (2002), no. 7, 381-384 .
  • [13] Thompson, K. and Dray, T., Taxicab Angles and Trigonometry. Pi Mu Epsilon J. 11 (2000), no. 2, 87-97 .
  • [14] Wallen, L. J., Kepler, The Taxicab Metric, and Beyond: An isoperimetric Primer. The College Mathematics Journal 26 (1995), no. 3, 178-190.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

S. Ekmekçi

Z. Akça Bu kişi benim

K. Altıntaş Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2015
Gönderilme Tarihi 12 Mart 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

APA Ekmekçi, S., Akça, Z., & Altıntaş, K. (2015). ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Mathematical Sciences and Applications E-Notes, 3(2), 27-33. https://doi.org/10.36753/mathenot.421326
AMA Ekmekçi S, Akça Z, Altıntaş K. ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Math. Sci. Appl. E-Notes. Ekim 2015;3(2):27-33. doi:10.36753/mathenot.421326
Chicago Ekmekçi, S., Z. Akça, ve K. Altıntaş. “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”. Mathematical Sciences and Applications E-Notes 3, sy. 2 (Ekim 2015): 27-33. https://doi.org/10.36753/mathenot.421326.
EndNote Ekmekçi S, Akça Z, Altıntaş K (01 Ekim 2015) ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Mathematical Sciences and Applications E-Notes 3 2 27–33.
IEEE S. Ekmekçi, Z. Akça, ve K. Altıntaş, “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”, Math. Sci. Appl. E-Notes, c. 3, sy. 2, ss. 27–33, 2015, doi: 10.36753/mathenot.421326.
ISNAD Ekmekçi, S. vd. “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”. Mathematical Sciences and Applications E-Notes 3/2 (Ekim 2015), 27-33. https://doi.org/10.36753/mathenot.421326.
JAMA Ekmekçi S, Akça Z, Altıntaş K. ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Math. Sci. Appl. E-Notes. 2015;3:27–33.
MLA Ekmekçi, S. vd. “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”. Mathematical Sciences and Applications E-Notes, c. 3, sy. 2, 2015, ss. 27-33, doi:10.36753/mathenot.421326.
Vancouver Ekmekçi S, Akça Z, Altıntaş K. ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Math. Sci. Appl. E-Notes. 2015;3(2):27-33.

Cited By

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