Convexification

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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.

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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.

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Contributed by: Robert Dickau, George Beck (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

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.



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