Relations on lines as primitive notions for Euclidean geometry

Basic Notions of Geometry and 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 ...

Notes on Euclidean Geometry Contents

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...

Response: of pigs and primitive notions.

I agree with Gary Comstock's conclusion that Ilu: research program at Beltsville is not morally justified. Moreover, I have no substantial disagreement with the demils of his clear, closely-reasoned argument. However, it seems to me that two aspects of Comstock's argument call for further consideration and commentary, both because of their intrinsic philosophical interest and because they are t...