A Non-Euclidean Story or: How to Persist When Your Geometry Doesn’t

Euclidean Geometry before non-Euclidean Geometry

In [3], in my argument for the primacy of Euclidean geometry on the basis of rigid motions and the existence of similar but non-congruent triangles, I wrote the following: A: “The mobility of rigid objects is now recognized as one of the things every normal human child learns in infancy, and this learning appears to be part of our biological progaramming.” B. “. . . we are all used to thinking ...

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Non - Euclidean Geometry ,

When and How to Imitate Your Neighbours

This paper summarises some previously published work on imitation, experimentation (or innovation) and aspiration thresholds using the FEARLUS modelling system and reports new work with FEARLUS extending these studies. Results are discussed in the context of existing literature on imitation and innovation in related contexts. A form of imitation in which land uses are selected on the criterion ...

To persist or not to persist ?

Ecological vector fields ẋi = xifi(x) on the non-negative cone Rn+ on R are often used to describe the dynamics of n interacting species. These vector fields are called permanent (or uniformly persistent) if the boundary ∂Rn+ of the nonnegative cone is repelling. We construct an open set of ecological vector fields containing a dense subset of permanent vector fields and containing a dense subs...