Modern physical theories tell us that space is not euclidean. Yet, to most people, euclidean geometry seems most natural. Furthermore, most mathematical theories of non-euclidean geometry refer back to euclidean geometry in one way or another. For example, in differential geometry, the differential areas are almost always approximately Euclidean. Why is this? I want to suggest here a reason roo...

In this paper, we study fuzzy substructures in connection withHv-structures. The original idea comes from geometry, especially from thetwo dimensional Euclidean vector space. Using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. We connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as Hv-groups...

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis o...

We are all familiar with Euclidean geometry and with the fact that it describes our three dimensional world so well In Euclidean geometry the sides of objects have lengths inter secting lines determine angles between them and two lines are said to be parallel if they lie in the same plane and never meet Moreover these properties do not change when the Euclidean transformations translation and r...

After the introduction of coordinates, it became possible to treat figures in plane and space by analytical methods, and calculus has been the main means for the study of curved figures. For example, one attaches the tangent line to a curve at each point. One sees how tangent lines change with points of the curve and gets an invariant called the curvature. C. F. Gauss, with whom differential ge...