Question 129
Tweaking a convex $n$ corner means the following: You select two adjacent sides $AB$ and $BC$ and replace them with the line $AM$, $MN$, $NC$, where $M \in AB$ and $N \in BC$ are arbitrary points in the Inside these routes are. In other words, you cut off a corner and get a $(n+1)$ corner.
Starting from a regular hexagon $\mathcal{P}_6$ with area 1, a sequence $\mathcal{P}_6, \mathcal{P}_7, \mathcal{P}_8, \ldots$ of convex polygons is created by continuous pinching. Show that the area of $\mathcal{P}_n$ is larger than $\frac{1}{2}$ for all $n \geq 6$, regardless of how zwacking is done.
Starting from a regular hexagon $\mathcal{P}_6$ with area 1, a sequence $\mathcal{P}_6, \mathcal{P}_7, \mathcal{P}_8, \ldots$ of convex polygons is created by continuous pinching. Show that the area of $\mathcal{P}_n$ is larger than $\frac{1}{2}$ for all $n \geq 6$, regardless of how zwacking is done.