Chromatic number of Euclidean plane

TL;DR

This paper discusses the longstanding question of the exact chromatic number of the Euclidean plane, highlighting apparent contradictions with planar graph coloring and aiming to clarify its precise value.

Contribution

The paper offers a new perspective on the chromatic number of the Euclidean plane, proposing insights that could resolve existing contradictions in the field.

Findings

Highlights the contradiction between plane chromatic number and planar graph coloring

Proposes a new approach to determine the exact chromatic number of the plane

Contributes to the ongoing debate on the plane's chromatic number

Abstract

If the chromatic number of Euclidean plane is larger than four, but it is known that the chromatic number of planar graphs is equal to four, then how does one explain it? In my opinion, they are contradictory to each other. This idea leads to confirm the chromatic number of the plane about its exact value.