Each of the following pictures contains a green regular polygon at the
center. In each picture, as the blue triangle moves, it always has the
same area, and its area is minimal among all circumscribed triangles for
the green polygon. Note that there is such a triangle that has one side
contained in every supporting line of the green
polygon. This property is shared by circles, ellipses, regular polygons
with number of sides not congruent to 0 mod 3 (and their images under
affine maps of the plane).
Square:
Pentagon:
Heptagon:
Octagon:
Decagon:
hendecagon:
triskaidecagon:
tetrakaidecagon:
