Real Examples of NeutroGeometry & AntiGeometry

Abstract

: For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems,
etc.) are totally (100%) true. But, in the real world, many items are not totally true. The
NeutroGeometry is a geometrical space that has some items that are only partially true (and partially
indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical
space that has some item that are totally (100%) false. While the Non-Euclidean Geometries
[hyperbolic and elliptic geometries] resulted from the total negation of only one specific axiom
(Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in
general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in
general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.),
and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea,
etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries. [5]