All Questions

We are given a set $X$ of $n\ge 3$ points in $\mathbb{R}^2$, belonging to the boundary of the convex hull of $X$ itself. Let $\Gamma(X)$ be the set of all convex, simple closed curves in $\mathbb{R}^2$...

I learn that Geometry has several categories/subfields from Wikipedia. But I am still not clear about the standards according to which they are classified. It seems Euclidean Geometry, Affine ...