On the Möbius geometry of Euclidean triangles

Triangles in Euclidean Arrangements

The number of triangles in arrangements of lines and pseudolines has been object of some research Most results however concern arrangements in the projective plane In this article we add results for the number of triangles in Euclidean arrange ments of pseudolines Though the change in the embedding space from projective to Euclidean may seem small there are interesting changes both in the resul...

On the Geometry of Equilateral Triangles

By studying the distances of a point to the sides, respectively the vertices of an equilateral triangle, certain new identities and inequalities are deduced. Some inequalities for the elements of the Pompeiu triangle are also established.

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 ...

On the Homogeneous Model of Euclidean Geometry

We attach the degenerate signature (n,0,1) to the dual Grassmann algebra of projective space to obtain a real Clifford algebra which provides a powerful, efficient model for euclidean geometry. We avoid problems with the degenerate metric by constructing an algebra isomorphism between the Grassmann algebra and its dual that yields non-metric meet and join operators. We focus on the cases of n=2...

Notes on Euclidean Geometry Contents