A simple equation giving shapes between a circle and a regular N-sided polygon

摘要

Precipitates in alloys often have nearly polyhedral shapes with round corners. To describe such shapes by a two-dimensional model, a simple equation giving intermediate shapes between a circle and a regular N-sided polygon is derived. It is shown that the intermediate shapes, called pseudo-polygons in the present study, are convex. The area of the pseudo-polygons is discussed.