TL;DR
This paper investigates the smallest triangles that can contain regular polygons like squares, pentagons, and hexagons, expanding previous work on maximum area polygons within triangles, using dynamic software for illustrations.
Contribution
It introduces a new problem of finding minimal-area triangles containing regular polygons, complementing prior work on maximum area polygons within triangles.
Findings
Identified smallest triangles containing regular polygons
Used Dynamic Software Sketchpad for all examples
Provided geometric constructions and bounds
Abstract
The first two installments of this series of papers dealt with the maximum area polygons: Parallelogram, Rectangle, Square or Equilateral Triangle, in given triangles. Minimum area polygons were also considered in the second paper on Equilateral Triangles. In this paper the puzzle will be turned the other way around. Given the regular unit polygons, a Square, Pentagon, or Hexagon, we searched for the smallest area triangle(s) which contains it. The Dynamic Software Sketchpad v5.10 BETA was used for all examples and figures throughout the work.
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Taxonomy
Topics3D Modeling in Geospatial Applications · Mathematics and Applications