Reasoning in Euclidean Geometry using Information Invariance Principle

This article presents an introduction to a new logical reasoning method for Euclidean geometry basedon the invariance principle of information (data). Due to this principle, any geometrical configuration(shape or entity) in Euclidean geometry possesses a conserved content of geometrical data that could beexpressed as information bits. On the basis of this principle, we explain what is the content of informationbits and how is the analysis of this content in Euclidean geometry. Every geometric structure is actually aset of information bits that define that structure. We discuss the relationship between bits of informationwith the use of straight edge and compass in Euclidean geometry and show that theorems of Euclideangeometry can be expressed in the term of bits of information. In this regard, we show that the abilityto draw a geometric structure, as well as theorems and propositions related to these structures, can bereduced to the rules of the invariance of information bits, and consequently leads to a new reasoningmethod in Euclidean geometry that can be applied for reasoning algorithms in AI. Based on this principlethe converse of corresponding angles postulate and some of the theorems of constructible numbers andregular polygons are proved with concise proofs.