A pseudo-Euclidean geometry

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 ...

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains

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...

A problem in Euclidean Geometry

I describe below an elementary problem in Euclidean (or Hyperbolic) geometry which remains unsolved more than 10 years after it was first formulated. There is a proof for n = 3 and (when the ball is the whole of 3-space) when n = 4. There is strong numerical evidence for n 6 30. Let (x1, x2, ...xn) be n distinct points inside the ball of radius R in Euclidean 3-space. Let the oriented line xixj...

Basic Notions of Geometry and Euclidean Geometry