Convexification

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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]

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send