×

Apollonian sets in taxicab geometry. (English) Zbl 1450.51002

The authors introduce Apollonian sets in the taxicab plane, recognize that these sets fit into a more general framework, and they establish a number of foundational facts about them. The authors provide a complete characterization of all Apollonian sets.

MSC:

51M05 Euclidean geometries (general) and generalizations
51M15 Geometric constructions in real or complex geometry
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] T. Erm\.i\commaaccents, Ö. Gel\.i\commaaccentsgen\serialcomma \andword A. Ek\.ic\.i, “A taxicab version of a triangle”s apollonius circle”, Journal of Mahani Mathematical Research Center 7:1 (2018), 25-36.
[2] R. Kaya \andword H. B. Colakoglu, “Taxicab versions of some Euclidean theorems”, Int. J. Pure Appl. Math. 26:1 (2006), 69-81. \xoxMR2205737 \xoxZBL1090.51501 · Zbl 1090.51501
[3] R. Kaya, Z. Akça, I. Günaltili\serialcomma \andword M. Özcan, “General equation for taxicab conics and their classification”, Mitt. Math. Ges. Hamburg 19 (2000), 135-148. \xoxMR1805591 · Zbl 0994.51007
[4] I. Kocayusufoğlu \andword E. Özdamar, “Isometries of taxicab geometry”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 47:1-2 (1998), 73-83. \xoxMR1698591 \xoxZBL0945.51008 · Zbl 0945.51008
[5] E. F. Krause, “Taxicab geometry”, The Mathematics Teacher 66:8 (1973), 695-706.
[6] B. E. Reynolds, “Taxicab Geometry”, Pi Mu Epsilon Journal 7:2 (1980), 77-88. \xoxZBL0439.51006 · Zbl 0439.51006
[7] D. J. Schattschneider, “The taxicab group”, Amer. Math. Monthly 91:7 (1984), 423-428. \xoxMR759218 \xoxZBL0564.51005 · Zbl 0564.51005
[8] J. R. Smart, Modern geometries, Brooks/Cole, 1998. \xoxZBL0863.51001 · Zbl 0863.51001
[9] K. P. Thompson, “The nature of length, area, and volume in taxicab geometry”, Int. Electron. J. Geom. 4:2 (2011), 193-207. \xoxMR2929589 \xoxZBL1308.51014 · Zbl 1308.51014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.