Journal of Geometry

, Volume 104, Issue 2, pp 229–255

# Isoperimetric triangular enclosures with a fixed angle

• Prosenjit Bose
• Jean-Lou De Carufel
Article

## Abstract

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.

51-04 51N20

## Keywords

Geometric optimization enclosing problems isoperimetric problems computational geometry

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