Abstract: In this activity, we’ll begin by exploring a set of foundational origami operations called the Huzita-Justin Axioms (HJA). Next, we’ll construct something called the Beloch square, which applies our concrete understanding of the HJA. Then, we’ll switch gears somewhat abruptly and talk about a geometric method to finding roots to polynomials with real-valued coefficients in one variable, called Lill’s method. Lastly, as the crux of this activity, we’ll prove an interesting connection between Lill’s method on such a polynomial of degree three and the Beloch square. If time and interest permits, we’ll also hear a brief epilogue on attempts at generalizing origami construction for broader goals, such as to solve real univariate polynomials of arbitrary degree.
