Math IA Help (Gini Coefficient/Lorenz Curve)

Good-day!

The concept of inequality, with the Lorenz Curve, Gini Coefficient, Kuznets Curve, etc. have fascinated me, and I am highly motivated to write my mathemetics IA about the Gini Coefficient. Though I’m not out to get low marks, so I’m looking for a, let’s just say topic or research question, that could get the most out of this IA.

I was thinking of comparing India and the USA, and deriving the Gini coefficient from Lorenz Curve. I just wonder how much actual mathematics this will require me to do, other than just using calculus to get the area?

In what approach do I show a lot of math in this IA? And what would be an effective topic/research question that would ultimately get me high marks in this manner?

THANK YOU (:

what did you end up getting for your draft?