Let me start my blog by revisiting my joint paper with Michel Helfgott, “Angles, Area, and Perimeter Caught in a Cubic” (published a year ago in Forum Geometricorum). In that paper we show that the angles of any triangle of area **A** and perimeter **P** are bounded by the *vertex* angles of the two *isosceles* triangles of area **A** and perimeter **P**. In addition to a wish to release this result from the title’s cubic, that is to provide a purely geometrical proof of it, I would like to suggest possible generalizations in two directions:

(I) Similar results for quadrilaterals, pentagons, etc: are there two special n-gons playing, for each n, the role of the two isosceles triangles (in the bounding now of the angles of all n-gons of area **A** and perimeter **P**)?

(II) Moving now to convex planar sets, can one replace angles by curvature, and find two special convex sets providing bounds for it? [Possibly an ill-posed question: one may always flatten the set somewhere in order to get a zero curvature — but, assuming smoothness everywhere, the question on the *upper* bound (on the curvature of a closed curve of area **A** and perimeter **P**) remains valid,]

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