An Algebraic Approach to Neutrosophic Euclidean Geometry

The objective of this paper is to present a general definition of Neutrosophic Euclidean geometry. The mechanism of comparison between neutrosophic numbers is introduced, as well as the absolute value is extended to the neutrosophical case. In addition, the concept of the neutrosophic plane with 𝑛 neutrosophic dimensions is obtained. Also, Euclidean geometric concepts are extended neutrosophically such as neutrosophic distance, neutrosophic midpoint, neutrosophic vectors, neutrosophic circles, and lines. A connection between neutrosophic geometrical concepts and classical Euclidean geometry is described and established.