Geometric Algebras for Euclidean Geometry

Conformal Geometry, Euclidean Space and Geometric Algebra

Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to programming complicated geometrical operations. But there is a fundamental weakness in this approach — the Euclidean distance between points is not handled in a s...

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...

Class Notes for Math 3400: Euclidean and Non-euclidean Geometry

We discuss aspects of Euclidean geometry including isometries of the plane, affine tranformations in the plane and symmetry groups. We then explore similar concepts in the sphere and projective space, and explore elliptic and hyperbolic geometry.

Basic Notions of Geometry and Euclidean Geometry