JOURNAL ARTICLE

Optimal Embedded and Enclosing Isosceles Triangles.

  • Published In: International Journal of Foundations of Computer Science, 2023, v. 34, n. 7. P. 737 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Ambrus, Áron; Csikós, Mónika; Kiss, Gergely; Pach, János; Somlai, Gábor 3 of 3

Abstract

Given a triangle Δ , we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of Δ with respect to area and perimeter. This problem was initially posed by Nandakumar [17, 22] and was first studied by Kiss, Pach, and Somlai [13], who showed that if Δ ′ is the smallest area isosceles triangle containing Δ , then Δ ′ and Δ share a side and an angle. In the present paper, we prove that for any triangle Δ , every maximum area isosceles triangle embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles Δ whose minimum perimeter isosceles containers do not share a side and an angle with Δ. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Foundations of Computer Science. 2023/11, Vol. 34, Issue 7, p737
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2023
  • ISSN:0129-0541
  • DOI:10.1142/S012905412342008X
  • Accession Number:173182848
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