For a simply connected polygon , convexification is the process of taking the convex hull of and then, for any side of that is not part of , reflecting the part of inside over the segment . Iterating the process eventually leads to a convex shape.[more]
Z. A. Melzak conjectured that a given iteration of the Koch snowflake requires the greatest number of convexifications to make a convex figure, compared to other figures with the same number of sides.[less]
Snapshot 1: a regular star requires only one convexification to become a convex figure
Snapshots 2, 3: the convexification of a figure often appears unlike the original figure
Reference: Z. A. Melzak, Invitation to Geometry, Mineola, NY: Dover, 2008.
Wolfram Demonstrations Project
Published: March 7 2011