Cyclic polygons in non-Euclidean geometry

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...

Cyclic Polygons in Classical Geometry

Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.

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 ...

The toric geometry of triangulated polygons in Euclidean space

Speyer and Sturmfels [SpSt] associated Gröbner toric degenerations Gr2(C) of Gr2(Cn) to each trivalent tree T with n leaves. These degenerations induce toric degenerations M r of Mr, the space of n ordered, weighted (by r) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers as stratified symplectic spaces and describe ...

Non - Euclidean Geometry ,