I am home! :) (Finally I have a descent computer/internet connection...) Now, to address concerns:

I'm uploading a newer version of my blog post now.

Version 2 of my entry: drive.google.com/file/d/0B74VpG3Y19fpMEFudXlGZ0VBczg/…

Regarding applications: I totally understand the desire for a more concrete application. I guess my (internalized) reason for writing the blog entry was to demonstrate that Green's Theorem has application for "discrete-ish" cases (I always thought of Green's theorem with regards to smooth curves, not piecewise-smooth). I've changed my old "Application" section to "Example," and added 3 outlines of "real-world" scenarios under the "Possible Application" sections.

Yes, it is $\LaTeX$.

(And TikZ graphics)

@vzn Uh, yeah. I did derive it myself after seeing some random assignment sheet on Green's Theorem online saying "Further problems: Derive a formula for the area of a polygon. (Hint: break into piecewise smooth sections)" or something like that. It's the same as Wikipedia's formula if you telescope mine.

So, in other words, I didn't really use any other sources other than someone saying "Try this problem:" (no solution given), and Wolfram Alpha's definitions of Green's Theorem, and Simple Polygon.

@vzn Yes, it does work on any simple polygon. That is, it doesn't matter if it's convex/concave, but the main concern is that it can't cross itself.

hi AN. nice! looks like you have incorporated most feedback.

a brief note that its not limited to convex polygons might be helpful. it seems in geometry some formulas or calculations are affected by concave vs convex polygons.

if you have seen the same formula anywhere else, a ref to that would be helpful.