Tweaking a convex n-gon means the following: choose two adjacent sides AB and BC and replaces them with the line segment AM, MN, NC, where M∈AB and N∈BC are arbitrary points inside these segments. In other words, you cut off a corner and get an (n+1)-corner.
Starting from a regular hexagon P6 with area 1, by continuous Tweaks a sequence P6,P7,P8,... convex polygons. Show that Area of Pn for all n≥6 greater than 21 is, regardless of how tweaks takes place. geometryGeometric Inequalitiescombinatorial geometryconvex