Journal of Geometry

, Volume 104, Issue 2, pp 229–255 | Cite as

Isoperimetric triangular enclosures with a fixed angle

  • Prosenjit Bose
  • Jean-Lou De CarufelEmail author


In this paper, we study four variants of the famous isoperimetric problem. Given a set S of n > 2 points in the plane (in general position), we show how to compute in O(n 2) time, a triangle with maximum (or minimum) area enclosing S among all enclosing triangles with fixed perimeter and one fixed angle. We also show how to compute in O(n 2) time, a triangle with maximum (or minimum) perimeter enclosing S among all enclosing triangles with fixed area and one fixed angle. We also provide an Ω (n log n) lower bound for these problems in the algebraic computation tree model.

Mathematics Subject Classification (2010)

51-04 51N20 


Geometric optimization enclosing problems isoperimetric problems computational geometry 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

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