How To Define A Flat Plane: The fruit of reinventing wheels when studying Euclidean geometry

By studying in steps what a flat plane is, this paper shows that only six axioms are necessary for 2-dimensional Euclidean geometry until the Pythagorean Theorem: 1) the existence of stable space; 2) the existence of a straight line through any two points, 3) the existence of distance measurement between any two points; 4) the limitation of the space to 2-dimensional, 5) the repeated equivalence, and 6) the reflected equivalence.

Besides introducing major mathematical concepts to young readers, this paper focuses on the context and thought process to conclude these axioms, and necessary theorems to test mathematically whether a 2-dimensional space is flat or not. It can also be used as a short introduction to Euclidean geometry until Pythagorean Theorem.