Some interesting infinite sets are created:

[1] An infinite set of conics (in the case of an ellipse, is it convergent inwards, where?).

[2] An infinite set of symmetric hexagons (same question).

[3] An infinite set of vertices of the hexagons (find the paths on which they are arranged).

[4] An infinite set of foci of the conics (find the curve on which they are arranged).

The polar c

The whole configuration can be considered to start from a triangle LGH, formed by two consecutive sides of some hexagon and point P, the center of all hexagons. Take then the symmetric of the vertices of the triangle w.r. to P, defining the first (foundamental) hexagon, and repeat the whole construction. When does it happens that the analogous construction from another triangle, like G'H'L', gives the same infinite sets?

Symmetric_hexagons.html

Produced with EucliDraw© |