Variations on a Theorem of Haga

In its original form, Haga’s theorem provides a simple and elegant way for exact division of the side of a square into thirds; its proof relies upon the Pythagorean Theorem, triangle similarity, and first-degree equations, which makes it accessible to middle school students (for an English version, see [Haga 02, Haga et al. 08, Hull 06]). The obvious generalization of Haga’s theorem to other exact divisions needs only an additional (yet easy) algebraic manipulation.