Successive Averages of the Vertices of a Polygon

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

If the vertices (thought of as vectors) of a polygon are , then the midpoints of the sides are . These new points form the vertices of another polygon, and the midpoints of its sides are . This process can be repeated for iterations.

[more]

There is another variable, , the number of successive points around the polygon that can be averaged. Here are the next two initial averages (and ):

The original seven points are scattered randomly. For clarity, drag them to form a convex or star-shaped polygon and experiment with the controls.

[less]

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


Snapshots


Details



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