On the distance formulae in the generalized taxicab geometry

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ÇOLAKOĞLU H. B.

TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.3, ss.1578-1594, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1809-78
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1578-1594
  • Anahtar Kelimeler: Generalized taxicab distance, metric, generalized taxicab geometry, three dimensional space, n-dimensional space
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we first determine the generalized taxicab distance formulae between a point and a line and two parallel lines in the real plane, then we determine the generalized taxicab distance formulae between a point and a plane, two parallel planes, a point and a line, two parallel lines and two skew lines in three dimensional space, giving also the relations between these formulae and their well-known Euclidean analogs. Finally, we give the generalized taxicab distance formulae between a point and a plane, a point and a line and two skew lines in n-dimensional space, by generalizing the concepts used for three dimensional space to n-dimensional space.