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Shape Theory. III. Comparative Theory of Backgound Independence
Edward Anderson
Background Independence is the modern form of the relational side of the Absolute versus Relational Debate. Difficulties with its implementation form the Problem of Time. Its 9 fac…
Shape Theories. II. Compactness Selection Principles
Edward Anderson
Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own…
Shape Theories. I. Their Diversity is Killing-Based and thus Nongeneric
Edward Anderson
Kendall's Shape Theory covers shapes formed by points in upon quotienting out the similarity transformations. This theory is based on the geometry and topology o…
Geometry from Brackets Consistency
Edward Anderson
We argue for Brackets Consistency to be a `Pillar of Geometry', i.e. a foundational approach, other Pillars being 1) Euclid's constructive approach, 2) the algebraic approach, 3) t…
Shape Derivatives
Edward Anderson
Shape Theory, together with Shape-and-Scale Theory, comprise Relational Theory. This consists of -point models on a manifold , for which some geometrical automorphism group $…
Quadrilaterals in Shape Theory. II. Alternative Derivations of Shape Space: Successes and Limitations
Edward Anderson
We show that the recent derivation that triangleland's topology and geometry is from Heron's formula does not extend to quadrilaterals by considering Brahmagupta, Bretschneid…