Centroid of a polygon

Ryan Hirst
In response to a question on StackExchange...
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. ______ Uses: Centroid of a Triangle: http://www.geogebratube.org/material/show/id/93237