See the first two of the below (in reverse order) for my recent exposition of this.

## Shape (In)dependent Inequalities for Triangleland’s Jacobi and Democratic-Linear Ellipticity Quantitities

Abstract Sides and medians are both Jacobi coordinate magnitudes. These furthermore enter equably into the spherical coordinates on Kendall’s shape sphere and the Hopf coordinates. This motivates treating medians on the same footing as sides in the geometry of triangles and the ensuing Shape Theory. In this article, we consequently reformulate inequalities for the medians … Continue reading Shape (In)dependent Inequalities for Triangleland’s Jacobi and Democratic-Linear Ellipticity Quantitities

## Relational Variables for Graph Theory

Abstract We systematically consider simple relational variables — relative variables, ratio variables and dilatational variables — for Graph Theory. We apply these to simplifying graph inequalities and elucidating a large number Graph-Theoretically significant probability-valued variables. This material has further use in developing network stucture quantifiers. It represents interaction between Similarity Geometry, and basic Shape Theory … Continue reading Relational Variables for Graph Theory

## Dirac’s Algorithm for Constrained Systems from the perspective of Order Theory

Abstract Dirac based his theory of constrained systems on Linear Algebra foundations. It is a brackets-algebraic consistency procedure with multiple outcomes, including new constraints dropping out and redeclaring brackets becoming necessary (Dirac brackets). This procedure has not yet been edited, however, to caution about and remove scaffolding structures that turn out to not in general … Continue reading Dirac’s Algorithm for Constrained Systems from the perspective of Order Theory