Four-Way Turiyam based Characterization of Non-Euclidean Geometry

Prem Kumar Singh

Department of Computer Science and Engineering,

Gandhi Institute of Technology and Management-Visakhapatnam,

Andhra Pradesh 530045, India

ORCID: 0000-0003-1465-6572

Email:: premsingh.csjm@gmail.com;  premsingh.csjm@yahoo.com

Abstract

Recently, a problem is addressed while dealing the data with Non-Euclidean Geometry and its characterization. The mathematician found negation of fifth postulates of Euclidean geometry easily and called as Non-Euclidean geometry. However Riemannian provided negation of second postulates also which still considered as Non-Euclidean. In this case the problem arises what will happen in case negation of other Euclid Postulates  exists. Same time total total or partial negation of Euclid postulates fails as hybrid Geometry. It become more crucial in case the data is unknown, incomplete or exists beyond the three-way space as heteroclinic pattern. To understand this problem, the current paper tried to distinguish Euclidean, Non-Euclidean, Anti-Geometry, Neutrogeometry and Turiyam or Unknown geometry using the complement operator with an example.

Keywords: Consciousness; Euclidean geometry; knowledge representation; NeutroGeometry; Non-Euclidean; Turiyam Geometry; Unknown Graph.