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Congruent triangles in arrangements of lines

(2018) ARS MATHEMATICA CONTEMPORANEA. 14(2). p.359-373
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Abstract
We study the maximum number of congruent triangles in finite arrangements of I lines in the Euclidean plane. Denote this number by f (l). We show that f (5) = 5 and that the construction realizing this maximum is unique, f (6) = 8, and f (7) = 14. We also discuss for which integers c there exist arrangements on l lines with exactly c congruent triangles. In parallel, we treat the case when the triangles are faces of the plane graph associated to the arrangement (i.e. the interior of the triangle has empty intersection with every line in the arrangement). Lastly, we formulate four conjectures.
Keywords
Arrangement, congruent triangles

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Citation

Please use this url to cite or link to this publication:

Chicago
Zamfirescu, Carol. 2018. “Congruent Triangles in Arrangements of Lines.” Ars Mathematica Contemporanea 14 (2): 359–373.
APA
Zamfirescu, C. (2018). Congruent triangles in arrangements of lines. ARS MATHEMATICA CONTEMPORANEA, 14(2), 359–373.
Vancouver
1.
Zamfirescu C. Congruent triangles in arrangements of lines. ARS MATHEMATICA CONTEMPORANEA. 2018;14(2):359–73.
MLA
Zamfirescu, Carol. “Congruent Triangles in Arrangements of Lines.” ARS MATHEMATICA CONTEMPORANEA 14.2 (2018): 359–373. Print.
@article{8545505,
  abstract     = {We study the maximum number of congruent triangles in finite arrangements of I lines in the Euclidean plane. Denote this number by f (l). We show that f (5) = 5 and that the construction realizing this maximum is unique, f (6) = 8, and f (7) = 14. We also discuss for which integers c there exist arrangements on l lines with exactly c congruent triangles. In parallel, we treat the case when the triangles are faces of the plane graph associated to the arrangement (i.e. the interior of the triangle has empty intersection with every line in the arrangement). Lastly, we formulate four conjectures.},
  author       = {Zamfirescu, Carol},
  issn         = {1855-3966},
  journal      = {ARS MATHEMATICA CONTEMPORANEA},
  keyword      = {Arrangement,congruent triangles},
  language     = {eng},
  number       = {2},
  pages        = {359--373},
  title        = {Congruent triangles in arrangements of lines},
  url          = {https://amc-journal.eu/index.php/amc/article/view/982},
  volume       = {14},
  year         = {2018},
}

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