Non-simultaneous match-stick geometry

TL;DR

This paper demonstrates that any finite constructible point set in Euclidean geometry can also be constructed using non-simultaneous match-sticks, establishing an equivalence under specific postulates.

Contribution

It introduces a new match-stick construction model and proves its equivalence to classical Euclidean constructions using compass and ruler.

Findings

Match-stick constructions can replicate all Euclidean constructible points.

Euclidean axioms can be deduced from the match-stick postulates.

Non-simultaneous match-stick methods are sufficient for geometric constructions.

Abstract

The purpose of this paper is to prove that every finite set of points that can be constructed in the Euclidean plane by using a compass and a ruler can also be constructed by using unitary match-sticks in a non-simultaneous way and following to a certain set of postulates. To prove this, we will deduce the Euclidean axioms for our defined set of axioms.