Besides classical beginning square, several models are built from various different forms of paper. Among them, regular polygons are often used for geometric models or modules. A usual feature related to this kind of constructions is to get the largest regular polygon within a given square. A large number of folding procedures, exact or approximated, simple or complex, using more or less of the paper area, exists. The goal is herein to find the optimal polygon (i.e. the regular polygon which size is the largest one, within a given square). Several folding procedures are compared for the pentagon case; moreover, a new exact and optimal construction is proposed, while trigonometry is the main tool needed as well as the integer part.