%****************************************************************
\section{Summary}
%****************************************************************
In the first section, we have shown that uniform electron gases (UEGs) on a $D$-sphere are an attractive generalisation of $D$-jellium.
However, although it is pleasing to know that the spherical and conventional gases become equivalent in the thermodynamic limit, we believe that it is more important to recognise that they are \emph{not} equivalent for finite number of electrons.
This has immediate chemical ramifications, suggesting that the traditional jellium paradigm is suboptimal for modelling molecular densities, even in regions of space where the density is nearly uniform.

In the second section, using \textit{finite} UEGs (FUEGs), we have created a \textit{generalized} LDA (GLDA) exchange functional which only depends on the curvature of the Fermi hole $\alpha$.
We have also combined our newly-designed GLDA functional with a PBE-type GGA functional to create a new type of MGGAs that we have called \textit{factorizable} MGGAs (FMGGAs).

