Background of this question is that I recently stumbled over the problem of deforming polygons in area-preserving way, i.e. modifying the angles between adjacent edges while preserving edge-lengths, topological equivalence to a circle and size of enclosed area.

Questions:

Has that problem been encountered and worked on before?

I'am looking for existing work, because I encountered some interesting questions when investigating the problem, e.g. what the minimum number of edges of polygons allowing such deformations is (I conjecture that it must be six).What to do with the further questions I encountered?

Any pointers to articles or blogs related to the problem would be of help to me.

**Remark:**

I chose the preliminary term "churning" as an analogy to the approximately surface-area and volume preserving deformations of the stomach; I am however no native English speaker, so a more appropriate verb may exist.