Searching for Optimal Polygon - Remarks About a General Construction and Application to Heptagon and Nonagon

David Dureisseix (1)

1 ENS Cachan - École normale supérieure - Cachan

Results obtained in a first paper deal with positioning optimal polygons -- i.e. largest regular polygons within a square. Such polygons have two particularities: symmetry with respect to at least one diagonal of the square and the fact that each edge of the square touches one vertex of the polygon. The technique used for pentagon (building the stellated pentagon) can be generalised for any number of edges. Complete construction in this case still remains open. Nevertheless, it seems necessary to begin with the construction of an angle pi/n , which is then enough to build the optimal polygon with the technique proposed herein. With procedures for folding pi/7 and pi/9 that are described herein, examples of heptagon and nonagon are performed.

Mots clés: polygon containment; optimally nested polygons; origami

Domaines: Mathématiques générales [math.GM]; Géométrie métrique [math.MG]

David Dureisseix. Searching for Optimal Polygon - Remarks About a General Construction and Application to Heptagon and Nonagon. 1997. ⟨hal-01246939⟩