Sum of Exterior Angles 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.

You can move the vertices to create a polygon and add vertices by alt + clicking. When you move the "align" slider all the way to the right, exterior angles of the polygon are aligned on a unique point and forms a full angle, .

[more]

Blue colored angles represent counter-clockwise, i.e. positive, angle and orange ones are vice versa. For a positive directed simple polygon, convex positive angles are blue and concave ones are orange. Therefore their algebraic sum is . In general, for any polygon, convex or concave, simple or self-intersecting, this sum is , where is an integer, represents winding number. For example, for a pentagram and for butterfly shaped polygon .

[less]

Contributed by: Okay Arik (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