Uniquely constructed figures

TL;DR

This paper classifies all convex figures that are uniquely constructed, meaning any equidecomposable figure must be congruent, providing a comprehensive understanding of such figures for educational purposes.

Contribution

It provides a complete classification of convex uniquely constructed figures, a novel geometric characterization.

Findings

All convex uniquely constructed figures are classified.

The classification offers insights into geometric decomposability.

The paper serves as an educational resource for school students.

Abstract

A convex figures F is called uniquely constructed if it satisfies the following condition: if F equidecomposable to a convex figure G then F is congruent to G. We classify all convex uniquely constructed figures. The paper written primary for school students.