Congruent triangles in arrangements of lines

Carol T. Zamfirescu

Abstract


We study the maximum number of congruent triangles in finite arrangements of ℓ 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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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications