Extracting squares from any quadrilateral

TL;DR

This paper presents a simple geometric procedure to generate squares from any quadrilateral by iteratively transforming it, with a proof accessible at undergraduate level.

Contribution

It introduces a novel iterative method to produce squares from arbitrary quadrilaterals, expanding geometric construction techniques.

Findings

Generates parallelograms from any quadrilateral

Produces squares when starting from a parallelogram

Iterative application yields squares from any quadrilateral

Abstract

A procedure that generates parallelograms from any quadrilateral is presented. If the original quadrilateral is itself a parallelogram, then the procedure gives squares. Hence, when applied two times, this procedure generates squares from any quadrilateral. The proof needs only undergraduate level.