The accompanying text is here:
http://math.stackexchange.com/questions/90463/how-can-i-calculate-the-centroid-of-polygon
Notes:
So... GGB agrees with me: The red ring at is my formula, the small diamond inside is Centroid[Jerome].
As you can test for yourself, GGB allows self-intersecting polygons. But Slumberland knows his centroid is now wrong!
See how Centroid[Jerome] follows?
I am left with some questions:
1. How shall we define a self-intersecting polygon?
2. Are GGB's definitions valid?
3. Are they true?
I will provide a solution to the first question.
I suggest the answers to 2. and 3. are Yes, and No.
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Uses:
Centroid of a Triangle: http://www.geogebratube.org/material/show/id/93237